WEBVTT 00:00:06.400 --> 00:00:08.760 SRINI DEVADAS: All right, good morning, everyone. 00:00:08.760 --> 00:00:11.170 Oh, do we have a treat for you today. 00:00:11.170 --> 00:00:16.210 I'm going to publicize, for the first time, my hidden 00:00:16.210 --> 00:00:18.430 talent of mind reading. 00:00:18.430 --> 00:00:21.220 And since this is a magic trick, you know, 00:00:21.220 --> 00:00:23.710 every magician needs an assistant. 00:00:23.710 --> 00:00:27.100 And I want to introduce Billy Moses to you. 00:00:27.100 --> 00:00:28.810 Billy is a PhD student. 00:00:28.810 --> 00:00:30.520 He already has three degrees from MIT, 00:00:30.520 --> 00:00:32.840 but he wants a fourth, I guess. 00:00:32.840 --> 00:00:35.800 And so I'm going to turn it over to Billy, here. 00:00:35.800 --> 00:00:39.580 And Billy is going to sort of set things up. 00:00:39.580 --> 00:00:44.130 I'm just going to do my thing, which is read your minds, OK? 00:00:44.130 --> 00:00:44.990 So go ahead, Billy. 00:00:44.990 --> 00:00:47.365 BILLY MOSES: So what's going to happen is, I'm going to-- 00:00:47.365 --> 00:00:48.460 I have this card deck right here, 00:00:48.460 --> 00:00:50.290 normal card deck, perfectly normal cards. 00:00:50.290 --> 00:00:51.680 They're not in any weird order. 00:00:51.680 --> 00:00:53.830 You can see them. 00:00:53.830 --> 00:00:57.044 I'm going to give five people the opportunity to pull a card 00:00:57.044 --> 00:00:58.210 and then give it back to me. 00:00:58.210 --> 00:00:59.332 They can look at the card. 00:00:59.332 --> 00:01:00.790 Then what's going to happen is, I'm 00:01:00.790 --> 00:01:05.470 going to turn over four of these cards, show you the final card. 00:01:05.470 --> 00:01:08.425 And then Srini is trying-- going to try to guess the fifth card. 00:01:08.425 --> 00:01:10.360 SRINI DEVADAS: Well, but what I need you to do 00:01:10.360 --> 00:01:13.720 is, when I'm going to guess, I need all of you 00:01:13.720 --> 00:01:16.950 to really focus on that hidden card, I mean, in your heads, 00:01:16.950 --> 00:01:17.560 right? 00:01:17.560 --> 00:01:19.600 So I can't do individual mind reading, just 00:01:19.600 --> 00:01:21.070 in case you guys were worried. 00:01:21.070 --> 00:01:23.380 So if you think I'm wearing a terrible-colored shirt, 00:01:23.380 --> 00:01:25.510 I'm not going to know, OK? 00:01:25.510 --> 00:01:28.746 But if you all think of this hidden card, 00:01:28.746 --> 00:01:30.120 I'm going to be able to guess it. 00:01:30.120 --> 00:01:32.470 But so I need some help, all right? 00:01:32.470 --> 00:01:36.190 BILLY MOSES: OK, anyone wants to try pulling some of the cards? 00:01:36.190 --> 00:01:36.970 OK. 00:01:36.970 --> 00:01:37.490 SRINI DEVADAS: And I guess-- 00:01:37.490 --> 00:01:37.950 BILLY MOSES: Take your favorite card. 00:01:37.950 --> 00:01:38.192 SRINI DEVADAS: --I can step out-- 00:01:38.192 --> 00:01:38.483 BILLY MOSES: --it can be anywhere. 00:01:38.483 --> 00:01:39.420 SRINI DEVADAS: --here, right? 00:01:39.420 --> 00:01:39.910 BILLY MOSES: Yeah. 00:01:39.910 --> 00:01:40.730 SRINI DEVADAS: All right. 00:01:40.730 --> 00:01:42.010 BILLY MOSES: And look at it. 00:01:42.010 --> 00:01:44.230 Give it back to me once you've-- 00:01:44.230 --> 00:01:45.210 cool. 00:01:45.210 --> 00:01:46.600 Anyone else want to pick a card? 00:01:46.600 --> 00:01:47.433 Want to pick a card? 00:01:47.433 --> 00:01:47.967 Here you go. 00:01:47.967 --> 00:01:50.550 You can look at the full deck, look at whatever card you want, 00:01:50.550 --> 00:01:52.880 pick it, cool. 00:01:52.880 --> 00:01:54.630 SRINI DEVADAS: We're doing a little trick. 00:01:54.630 --> 00:01:55.352 BILLY MOSES: Anyone else want to pick a card? 00:01:55.352 --> 00:01:56.352 You want to pick a card? 00:02:02.223 --> 00:02:05.760 OK, anyone else want to pick a card? 00:02:05.760 --> 00:02:06.975 Want to pick a card? 00:02:11.340 --> 00:02:13.030 Cool, want to pick a card? 00:02:17.270 --> 00:02:25.030 Cool, OK, I've got my cards all nice together. 00:02:38.240 --> 00:02:40.782 OK, so five cards, I'm going to show you first. 00:02:40.782 --> 00:02:43.240 And then we're going to present them in a fun way for Srini 00:02:43.240 --> 00:02:43.740 to see. 00:02:43.740 --> 00:02:45.450 So the five cards are as follows. 00:02:45.450 --> 00:02:48.350 We have this wonderful Seven of Clubs. 00:02:48.350 --> 00:02:52.640 We have a Jack of Hearts. 00:02:52.640 --> 00:02:56.860 We have Seven of Hearts. 00:02:56.860 --> 00:02:59.570 We have Queen of Spades. 00:02:59.570 --> 00:03:01.674 And we have Ten of Clubs. 00:03:01.674 --> 00:03:03.340 Now, for the people who pulled the card, 00:03:03.340 --> 00:03:06.340 these are indeed the cards that you gave me, right? 00:03:06.340 --> 00:03:08.840 No one missed their card in the deck? 00:03:08.840 --> 00:03:10.390 OK, I'll go get Srini. 00:03:13.916 --> 00:03:15.540 SRINI DEVADAS: All right, ready for me? 00:03:15.540 --> 00:03:16.248 BILLY MOSES: Yup. 00:03:18.630 --> 00:03:25.350 OK, the first card is the Seven of Clubs. 00:03:25.350 --> 00:03:31.500 The second card is the Jack of Hearts. 00:03:31.500 --> 00:03:37.890 The third card is the Seven of Hearts. 00:03:37.890 --> 00:03:40.590 The fourth card is-- and this is the final card that Srini will 00:03:40.590 --> 00:03:42.960 be able to see-- 00:03:42.960 --> 00:03:45.330 the Queen of Spades. 00:03:45.330 --> 00:03:46.770 Now, everyone think to yourself. 00:03:46.770 --> 00:03:48.784 You've got to see the card, the fifth card, 00:03:48.784 --> 00:03:49.950 that Srini is going to have. 00:03:49.950 --> 00:03:52.560 Think it very closely in your mind, think. 00:03:52.560 --> 00:03:55.090 SRINI DEVADAS: All right, definitely a clubs, definitely 00:03:55.090 --> 00:03:56.400 a clubs-- 00:03:56.400 --> 00:03:59.325 OK, see-- and I'm getting-- 00:04:03.360 --> 00:04:05.580 I'm getting at Ten of Clubs. 00:04:05.580 --> 00:04:08.310 BILLY MOSES: And it is a Ten of Clubs. 00:04:08.310 --> 00:04:10.370 SRINI DEVADAS: All right, thank you. 00:04:14.350 --> 00:04:20.690 All right, so I guess I'll have to confess. 00:04:20.690 --> 00:04:24.650 I'm not a mind reader, but I also did not cheat, OK? 00:04:24.650 --> 00:04:27.230 So there's an algorithm here. 00:04:27.230 --> 00:04:29.600 And do you guys want to know what the algorithm is 00:04:29.600 --> 00:04:32.200 so you can go and try this out, I guess, 00:04:32.200 --> 00:04:36.530 when you go back home next, or whatever, at your dorms, 00:04:36.530 --> 00:04:39.680 or with your classmates? 00:04:39.680 --> 00:04:45.380 So it's not as easy as it might seem, simply 00:04:45.380 --> 00:04:49.580 because the combinations aren't really in our favor, right? 00:04:49.580 --> 00:04:53.540 So if you think about it, there's 52 cards. 00:04:53.540 --> 00:04:55.870 So this is a regular deck of cards. 00:04:55.870 --> 00:04:58.660 You know, it's as I said, there's no cheating here. 00:04:58.660 --> 00:05:01.765 Billy showed me four cards. 00:05:06.680 --> 00:05:18.439 So which means the fifth card could be 1 of 48, right? 00:05:18.439 --> 00:05:19.730 I mean, it's completely random. 00:05:19.730 --> 00:05:23.070 You guys picked these five cards completely at random, 00:05:23.070 --> 00:05:25.880 so there's no way that that fifth card could 00:05:25.880 --> 00:05:28.220 be anything specific, OK? 00:05:28.220 --> 00:05:33.590 So what Billy had to do was, in the four cards 00:05:33.590 --> 00:05:40.010 that he showed me, he really had to communicate one of-- 00:05:40.010 --> 00:05:44.470 specifically, one of 48 possibilities, 00:05:44.470 --> 00:05:46.000 which is kind of-- you know, if you 00:05:46.000 --> 00:05:48.374 look-- if you think about it, then the math doesn't quite 00:05:48.374 --> 00:05:50.016 work out, right? 00:05:50.016 --> 00:05:52.170 And so if you just say-- 00:05:52.170 --> 00:05:54.270 so what are the ways-- 00:05:54.270 --> 00:05:57.600 how much information could you imagine 00:05:57.600 --> 00:06:00.880 communicating, in terms of bits of information, right? 00:06:00.880 --> 00:06:03.210 You know, in terms of possibilities or bits, 00:06:03.210 --> 00:06:06.990 how much information do you think that Billy could 00:06:06.990 --> 00:06:09.766 communicate in these four cards, which 00:06:09.766 --> 00:06:10.890 were also picked at random. 00:06:10.890 --> 00:06:12.931 Obviously, they have to be specific cards, right? 00:06:12.931 --> 00:06:14.760 He just put them up there, right? 00:06:14.760 --> 00:06:17.010 So if I have four cards, what are the ways 00:06:17.010 --> 00:06:19.260 that Billy could communicate information. 00:06:19.260 --> 00:06:21.900 I mean, you saw what he did. 00:06:21.900 --> 00:06:22.540 Any ideas? 00:06:26.120 --> 00:06:27.820 Yeah, Ganatra? 00:06:27.820 --> 00:06:29.704 AUDIENCE: The order the cards are placed. 00:06:29.704 --> 00:06:31.620 SRINI DEVADAS: The order the cards are placed, 00:06:31.620 --> 00:06:33.422 so that's a great answer. 00:06:33.422 --> 00:06:35.880 But if you look at the order in which the cards are placed, 00:06:35.880 --> 00:06:38.780 how many different orderings are there? 00:06:38.780 --> 00:06:42.230 Four cards, how many different orderings? 00:06:42.230 --> 00:06:46.370 4 factorial, right, and that is? 00:06:46.370 --> 00:06:50.750 24, so I'm not quite at 48 yet, right? 00:06:50.750 --> 00:06:53.330 So that's a bit of a problem. 00:06:53.330 --> 00:06:56.020 So is there something else going on other than the ordering? 00:06:58.680 --> 00:06:59.205 Yeah? 00:06:59.205 --> 00:07:01.080 AUDIENCE: The time rate at which he put them. 00:07:04.294 --> 00:07:05.710 SRINI DEVADAS: So you mean the way 00:07:05.710 --> 00:07:09.700 he put them up, you know, slowly versus quickly? 00:07:09.700 --> 00:07:12.930 Or did you mean something with which was-- 00:07:12.930 --> 00:07:16.502 the time in terms of exposure of the cards, or? 00:07:16.502 --> 00:07:17.328 AUDIENCE: Have some variations, for example, whether the red is 00:07:17.328 --> 00:07:17.869 before black. 00:07:30.085 --> 00:07:32.460 SRINI DEVADAS: Well, but that's all part of the ordering. 00:07:32.460 --> 00:07:36.660 I mean, you have to be careful here, in that, I mean, 00:07:36.660 --> 00:07:38.550 you can't do both, right? 00:07:38.550 --> 00:07:40.650 I mean, you can't constrain the ordering 00:07:40.650 --> 00:07:44.040 and then say that there's 24 different orderings. 00:07:44.040 --> 00:07:46.350 The moment you constrain orderings, the number 00:07:46.350 --> 00:07:48.570 of orderings shrinks, right? 00:07:48.570 --> 00:07:53.144 So I will say that, as I said, this is a very legit trick. 00:07:53.144 --> 00:07:54.310 It's completely algorithmic. 00:07:54.310 --> 00:07:56.268 We're going to write code for it-- or I'm going 00:07:56.268 --> 00:07:58.350 to show you code for it. 00:07:58.350 --> 00:08:03.120 But there's nothing else other than the ordering, OK? 00:08:03.120 --> 00:08:05.680 He is-- there's no sleight of hand. 00:08:05.680 --> 00:08:08.046 There's no hidden communication. 00:08:08.046 --> 00:08:09.420 You know, he didn't stress words, 00:08:09.420 --> 00:08:12.000 you know, Clubs meant something, or you know, 00:08:12.000 --> 00:08:13.870 Spades meant something else. 00:08:13.870 --> 00:08:16.210 It was just the ordering, OK? 00:08:16.210 --> 00:08:21.854 And so there's a gap here in terms of 24 and 48, right? 00:08:21.854 --> 00:08:24.270 And so what's cool about this trick is that we're actually 00:08:24.270 --> 00:08:29.000 going to be able to do this original trick, 00:08:29.000 --> 00:08:31.980 where the fifth card could be one of 48, 00:08:31.980 --> 00:08:36.330 because we're going to do one thing that you probably 00:08:36.330 --> 00:08:40.630 didn't notice, because we only did the trick once, all right? 00:08:40.630 --> 00:08:43.890 And so let me explain how this is going to work, 00:08:43.890 --> 00:08:45.660 with just sort of randomly picking-- 00:08:45.660 --> 00:08:47.160 I'm just going pick the top 5 cards, 00:08:47.160 --> 00:08:48.870 assuming these are shuffled. 00:08:48.870 --> 00:08:51.520 And you can assume these things that are at random, right? 00:08:51.520 --> 00:08:55.000 So I have five cards that I've picked here. 00:08:55.000 --> 00:08:58.600 And can you all see them? 00:08:58.600 --> 00:09:02.355 OK, what do you notice about these five cards? 00:09:05.130 --> 00:09:07.625 Anything-- yup, Fadi. 00:09:07.625 --> 00:09:09.500 AUDIENCE: There are four types and five cards 00:09:09.500 --> 00:09:11.208 so there's at least one that is repeated. 00:09:16.010 --> 00:09:17.260 SRINI DEVADAS: Right, so the-- 00:09:17.260 --> 00:09:20.270 so you're saying the suit, right? 00:09:20.270 --> 00:09:21.500 So it is clear. 00:09:21.500 --> 00:09:22.250 This is true here. 00:09:22.250 --> 00:09:25.790 You have the Seven of Clubs and the Ten of Clubs, right? 00:09:25.790 --> 00:09:29.340 Oh are these the cards that you pulled out, or close? 00:09:29.340 --> 00:09:33.010 Anyway, so they look pretty similar to the ones we used, 00:09:33.010 --> 00:09:36.500 but that's probably just because we didn't shuffle the deck. 00:09:36.500 --> 00:09:39.800 But obviously, if you have five cards, 00:09:39.800 --> 00:09:43.640 and you only have four suits, I guess 00:09:43.640 --> 00:09:47.450 you could call it the pigeonhole principle from 6.042, 00:09:47.450 --> 00:09:50.120 but you're definitely going to have 00:09:50.120 --> 00:09:54.650 a pair of cards that are going to be of the same suit, right? 00:09:54.650 --> 00:09:58.030 I mean, there may be more than two cards of the same suit, 00:09:58.030 --> 00:10:00.990 but you're guaranteed, for any five cards-- 00:10:00.990 --> 00:10:02.435 let me just pick another five-- 00:10:02.435 --> 00:10:05.390 that two of them are going to be of the same suit, right? 00:10:05.390 --> 00:10:06.930 That's pretty much guaranteed. 00:10:06.930 --> 00:10:09.660 And so we ended up getting clubs again here. 00:10:09.660 --> 00:10:14.580 And so you have Two and Four of the same suit. 00:10:14.580 --> 00:10:17.420 So the first thing that happens in this trick 00:10:17.420 --> 00:10:22.710 is, we use the first card to give away the suit. 00:10:22.710 --> 00:10:26.840 Or Billy used the first card to give away the suit. 00:10:26.840 --> 00:10:32.090 Doesn't quite finish the story here, 00:10:32.090 --> 00:10:34.370 because let's just say that I'm going 00:10:34.370 --> 00:10:41.990 to use the first card to signify the suit. 00:10:47.090 --> 00:10:54.780 So in this case, let's just say I am going to do Clubs. 00:10:54.780 --> 00:10:58.260 Now, I have a choice here. 00:10:58.260 --> 00:11:04.850 I could-- Billy could have hidden Two, 00:11:04.850 --> 00:11:08.570 and showed me the Four of Clubs as the first card, right, 00:11:08.570 --> 00:11:09.804 or vice versa. 00:11:09.804 --> 00:11:11.720 And keep that in mind, because that's actually 00:11:11.720 --> 00:11:14.270 incredibly important. 00:11:14.270 --> 00:11:17.030 But if you just say that the first card is 00:11:17.030 --> 00:11:20.450 going to signify the suit, then let's 00:11:20.450 --> 00:11:22.520 say the suit is now out of the picture, 00:11:22.520 --> 00:11:25.730 so I know the suit of the card. 00:11:25.730 --> 00:11:32.100 How many-- so I have three cards left, all right? 00:11:32.100 --> 00:11:34.920 And I got a hidden card. 00:11:34.920 --> 00:11:41.250 I know the suit of the hidden card, but that card could be-- 00:11:41.250 --> 00:11:46.030 the hidden card-- how many possibilities are there 00:11:46.030 --> 00:11:47.870 for the hidden card now? 00:11:50.560 --> 00:11:51.970 How many possibilities? 00:11:51.970 --> 00:11:55.410 I mean, this is all at random. 00:11:55.410 --> 00:11:56.708 Well, 13. 00:11:56.708 --> 00:11:58.142 AUDIENCE: 12 00:11:58.142 --> 00:12:00.660 SRINI DEVADAS: Oh, good point, good, good, good-- 00:12:00.660 --> 00:12:03.510 see, this is exactly why I need attentive students. 00:12:03.510 --> 00:12:09.790 OK, good, so there's 12 possibilities since one of them 00:12:09.790 --> 00:12:10.510 was-- 00:12:10.510 --> 00:12:12.590 one of them was shown, right? 00:12:12.590 --> 00:12:15.650 So did that help us? 00:12:15.650 --> 00:12:18.460 There are three cards left, and so how many different-- 00:12:18.460 --> 00:12:20.830 I mean, the first card is the first card, 00:12:20.830 --> 00:12:23.950 so it's no longer part of this permutation. 00:12:23.950 --> 00:12:25.900 I can't count it in terms of the permutations. 00:12:25.900 --> 00:12:27.305 There's only three cards left. 00:12:27.305 --> 00:12:28.930 And those-- certainly those three cards 00:12:28.930 --> 00:12:32.440 could be ordered in a certain way, 00:12:32.440 --> 00:12:34.600 but how many combinations or permutations 00:12:34.600 --> 00:12:37.380 are there of three cards? 00:12:37.380 --> 00:12:41.850 Only six permutations, so again, I seem to have a problem here. 00:12:41.850 --> 00:12:46.020 I don't seem to have solved the original problem of the 24 00:12:46.020 --> 00:12:47.200 to 48. 00:12:47.200 --> 00:12:50.100 I still have a 6-12 gap, right? 00:12:50.100 --> 00:12:53.940 So we're going to have to somehow cover that gap. 00:12:53.940 --> 00:12:56.790 And any thoughts? 00:12:56.790 --> 00:12:58.170 I gave you a little bit of a hint 00:12:58.170 --> 00:13:01.290 as to how this gap is going to be covered when I talked 00:13:01.290 --> 00:13:03.630 about the Two and the Four. 00:13:03.630 --> 00:13:08.520 How am I going to cover this gap, the 6-12 gap? 00:13:15.870 --> 00:13:17.086 Yeah, Kanishka. 00:13:17.086 --> 00:13:17.783 AUDIENCE: Possibly by saying odd or even. 00:13:17.783 --> 00:13:20.408 So if the next card you can say odd or even you shrink it down. 00:13:24.047 --> 00:13:25.630 SRINI DEVADAS: But you mean-- say, you 00:13:25.630 --> 00:13:27.171 mean Billy is going to say something? 00:13:27.171 --> 00:13:29.280 AUDIENCE: No, he's going to present the next card. 00:13:29.280 --> 00:13:29.764 SRINI DEVADAS: Yeah. 00:13:29.764 --> 00:13:30.316 AUDIENCE: Whether it is thinking that the final card you have 00:13:30.316 --> 00:13:30.657 to guess is odd or even and you can shrink down 00:13:30.657 --> 00:13:31.407 the possibilities. 00:13:37.467 --> 00:13:39.800 SRINI DEVADAS: So, I mean, he-- the only thing he can do 00:13:39.800 --> 00:13:44.570 is give me an ordering of the remaining three cards, right? 00:13:44.570 --> 00:13:45.759 Yeah, go ahead. 00:13:45.759 --> 00:13:46.300 Kevin, right? 00:13:46.300 --> 00:13:47.966 AUDIENCE: Yeah, maybe you used the cards 00:13:47.966 --> 00:13:52.700 to make a low-to-high limit on the range. 00:13:52.700 --> 00:13:55.820 SRINI DEVADAS: That's good, and low-a-high limit on the range, 00:13:55.820 --> 00:13:57.990 exactly right. 00:13:57.990 --> 00:14:03.770 So what's happening here is, not only do I have the first card-- 00:14:03.770 --> 00:14:07.240 and it's not the first card is just giving me the suit. 00:14:07.240 --> 00:14:09.170 I mean, that's the way I said it, right? 00:14:09.170 --> 00:14:11.930 But the first card also has a number on it, right? 00:14:11.930 --> 00:14:13.770 The first card has a number on it. 00:14:13.770 --> 00:14:16.880 So that number could be an anchor 00:14:16.880 --> 00:14:21.950 that is going to help me figure out what the hidden card is, 00:14:21.950 --> 00:14:22.760 right? 00:14:22.760 --> 00:14:24.710 And what's important to understand, 00:14:24.710 --> 00:14:28.730 and this is really the last interesting point 00:14:28.730 --> 00:14:30.980 with respect to shrinking these possibilities 00:14:30.980 --> 00:14:37.190 or these permutations down, is you want to think about your-- 00:14:37.190 --> 00:14:42.680 let me draw this out properly in a nice little circle. 00:14:42.680 --> 00:14:49.470 You don't want to think about just a ascending sequence 00:14:49.470 --> 00:14:52.780 of cards or numbers. 00:14:52.780 --> 00:14:57.310 You want to think about this as being circular, as you'll see, 00:14:57.310 --> 00:14:58.660 for the following reason. 00:15:08.084 --> 00:15:11.382 All right, so let's just say the ace is a 1. 00:15:11.382 --> 00:15:12.840 And so we're going to think of that 00:15:12.840 --> 00:15:18.540 as being the smallest number, so you go 1 through 13, 00:15:18.540 --> 00:15:19.350 in this case. 00:15:19.350 --> 00:15:21.040 The king is a 13. 00:15:21.040 --> 00:15:22.750 All right, so that's your number. 00:15:22.750 --> 00:15:25.474 And so you could imagine you'd go 1 through 13. 00:15:25.474 --> 00:15:26.640 So let's just do that first. 00:15:26.640 --> 00:15:29.490 And then I'll explain to you why I drew it in a circle. 00:15:29.490 --> 00:15:34.830 And the first thing that happens is, 00:15:34.830 --> 00:15:38.320 I'm going to take some card here. 00:15:38.320 --> 00:15:42.160 And I'm going to make that the first card, 00:15:42.160 --> 00:15:44.420 so I don't care about suits anymore. 00:15:44.420 --> 00:15:47.490 And if I just picked this-- 00:15:47.490 --> 00:15:48.320 another five cards. 00:15:48.320 --> 00:15:52.060 Let's just do this again, but with another set of five cards. 00:15:52.060 --> 00:15:53.580 And what do I have here? 00:15:53.580 --> 00:15:57.170 Oh, I've got mostly hearts, OK. 00:15:57.170 --> 00:16:00.300 So let me do something more interesting. 00:16:00.300 --> 00:16:02.940 This is too many hearts here. 00:16:02.940 --> 00:16:05.040 Right, let's do this. 00:16:05.040 --> 00:16:10.200 So now, I got a Two and a Jack. 00:16:10.200 --> 00:16:12.360 And I got a Ten an an Eight. 00:16:12.360 --> 00:16:15.990 OK, now I'll make this even more interesting by picking-- 00:16:15.990 --> 00:16:17.260 I want to pick-- 00:16:17.260 --> 00:16:19.020 I want to get a hearts card. 00:16:19.020 --> 00:16:20.460 And let's see how this works. 00:16:26.196 --> 00:16:32.170 Ah finally, all right, so this is what I have, King of Hearts, 00:16:32.170 --> 00:16:34.090 the Eight of Spades, et cetera. 00:16:34.090 --> 00:16:39.460 So the two cards with the same suit are the Two and the Jack. 00:16:39.460 --> 00:16:43.520 And so here's the important thing. 00:16:43.520 --> 00:16:46.810 One of the things that Billy did, kind of, in a subtle way, 00:16:46.810 --> 00:16:51.160 I'm assuming, and some of you may have picked up on it. 00:16:51.160 --> 00:16:54.580 The very first card that he asked one of you 00:16:54.580 --> 00:16:57.700 to pick certainly wasn't the hidden card, right? 00:16:57.700 --> 00:16:59.860 I mean, he got all five cards. 00:16:59.860 --> 00:17:03.070 And then he decided which of the cards 00:17:03.070 --> 00:17:05.270 was going to be the hidden card and then took 00:17:05.270 --> 00:17:08.319 the remaining four cards and encoded them. 00:17:08.319 --> 00:17:11.710 And if you don't do that, if you just say this, if you-- 00:17:11.710 --> 00:17:15.640 this trick won't work if this is the hidden card. 00:17:15.640 --> 00:17:19.569 This trick is only going to work as it turns out 00:17:19.569 --> 00:17:24.160 if the hidden card is a Two. 00:17:24.160 --> 00:17:30.910 It won't even work if the hidden card is a Jack. 00:17:30.910 --> 00:17:32.520 And there's a reason for that. 00:17:32.520 --> 00:17:36.040 And you-- can you think of the reason for that 00:17:36.040 --> 00:17:37.819 if you look at the board? 00:17:37.819 --> 00:17:39.360 Can you think of the reason for that? 00:17:39.360 --> 00:17:41.122 Someone other than Fadi? 00:17:44.426 --> 00:17:47.260 Someone else? 00:17:47.260 --> 00:17:48.920 What do you see up here? 00:17:48.920 --> 00:17:50.150 So what am I trying to do? 00:17:50.150 --> 00:17:52.550 In terms of-- what would happen-- 00:17:52.550 --> 00:17:53.720 you guys talked about-- 00:17:53.720 --> 00:17:56.040 Kevin mentioned distance and things like that, right? 00:17:56.040 --> 00:17:57.630 You know, you call it the offset. 00:17:57.630 --> 00:18:05.840 So what would happen if I hid the Jack, and I did this-- 00:18:05.840 --> 00:18:08.000 I did something like this, where I-- 00:18:08.000 --> 00:18:11.540 the Two of Diamonds was the first card that was put out. 00:18:11.540 --> 00:18:15.080 And then I tried to encode and number 00:18:15.080 --> 00:18:16.610 using these remaining three cards, 00:18:16.610 --> 00:18:19.160 what's the biggest number that I could encode? 00:18:19.160 --> 00:18:20.270 I mean, in-- 00:18:20.270 --> 00:18:25.240 I need to encode lots of numbers, right? 00:18:25.240 --> 00:18:27.970 So what's the biggest number that I could encode here? 00:18:27.970 --> 00:18:30.700 If I had six permutations, and I start with one, 00:18:30.700 --> 00:18:35.110 the biggest number that I could encode is a 6, right? 00:18:35.110 --> 00:18:40.240 Sadly, the Jack is too far away from the two, right? 00:18:40.240 --> 00:18:45.130 If I think of the Jack as being an 11, it's 9 away from the 2, 00:18:45.130 --> 00:18:46.040 right? 00:18:46.040 --> 00:18:50.030 But help me out here, what could I do? 00:18:50.030 --> 00:18:53.704 If I flipped it, what happens? 00:18:53.704 --> 00:18:55.150 AUDIENCE: Count backwards 00:18:55.150 --> 00:18:56.858 SRINI DEVADAS: You could count backwards. 00:18:56.858 --> 00:18:59.007 Or what do I have up there on the board? 00:18:59.007 --> 00:19:00.590 What do you see up there on the board? 00:19:04.684 --> 00:19:06.100 I wrote something that was linear, 00:19:06.100 --> 00:19:10.050 but what do I have up there on the left? 00:19:10.050 --> 00:19:13.750 Circular, so you think mod, mod arithmetic you know, think 00:19:13.750 --> 00:19:16.180 of this as being circular, OK? 00:19:16.180 --> 00:19:26.050 So what happens is that, if I picked a 2 and a Jack, if I-- 00:19:26.050 --> 00:19:28.390 what I want to do is to go clockwise. 00:19:28.390 --> 00:19:36.980 OK and because there are only 13 cards, for any pair of cards, 00:19:36.980 --> 00:19:42.710 it's always the case that I can choose the first card in such 00:19:42.710 --> 00:19:46.280 a way that the hidden card is, at most, 6 00:19:46.280 --> 00:19:50.270 away from the first card, OK? 00:19:50.270 --> 00:19:54.380 Because you could get into a situation where, 00:19:54.380 --> 00:19:59.630 obviously, if I ended up hiding the Jack and exposing the 2, 00:19:59.630 --> 00:20:03.170 I end up getting a 9, which is impossible to encode. 00:20:03.170 --> 00:20:10.810 But if I hide the 2 and expose the Jack, then I go 1, 2, 3, 4, 00:20:10.810 --> 00:20:14.540 and I am at, basically, 4, OK? 00:20:14.540 --> 00:20:16.520 So that's the last thing. 00:20:16.520 --> 00:20:18.080 So let's just do this really quickly 00:20:18.080 --> 00:20:22.100 with yet another set of five cards. 00:20:22.100 --> 00:20:25.590 Now obviously we practiced so we could do this fairly quickly, 00:20:25.590 --> 00:20:26.090 right? 00:20:26.090 --> 00:20:29.600 But-- and you can practice too, but sometimes with things you 00:20:29.600 --> 00:20:33.196 get lucky, you know, and you get easy things to encode. 00:20:33.196 --> 00:20:34.070 So what happens here? 00:20:34.070 --> 00:20:37.550 Someone wants to-- so now that you know the algorithm, 00:20:37.550 --> 00:20:40.700 you have some choices here, but obviously you have-- 00:20:40.700 --> 00:20:41.960 not all choices would work. 00:20:41.960 --> 00:20:43.790 You've got to be a little bit careful. 00:20:43.790 --> 00:20:47.920 What would you hide? 00:20:47.920 --> 00:20:50.570 So you need to make sure that you get-- 00:20:50.570 --> 00:20:52.202 you can choose a pair of-- 00:20:52.202 --> 00:20:53.660 I'll make this a little bit easier. 00:20:58.600 --> 00:21:04.390 Sometimes choices make things more difficult. 00:21:04.390 --> 00:21:08.700 Perfect, all right, so what you see here is-- 00:21:08.700 --> 00:21:10.930 you know that you have to do the clubs now, 00:21:10.930 --> 00:21:15.520 because you have the clubs as being the suit that's repeated. 00:21:15.520 --> 00:21:17.920 No other suits are repeated, right? 00:21:17.920 --> 00:21:20.590 So what am I going to expose? 00:21:20.590 --> 00:21:22.330 And what am I going to hide? 00:21:22.330 --> 00:21:25.250 That's your first question, right? 00:21:25.250 --> 00:21:27.560 Someone else? 00:21:27.560 --> 00:21:29.560 You guys are all going to have to do this trick. 00:21:29.560 --> 00:21:31.870 That's the final exam for this class. 00:21:31.870 --> 00:21:36.850 On Friday next week, you're all doing the trick-- no. 00:21:36.850 --> 00:21:38.720 So what am I going to-- 00:21:38.720 --> 00:21:39.670 yeah, go ahead, Josh? 00:21:39.670 --> 00:21:42.923 AUDIENCE: You are going to hide the Ace, the King of Clubs 00:21:42.923 --> 00:21:44.150 would be the first card. 00:21:44.150 --> 00:21:46.608 SRINI DEVADAS: You're going to hide the Ace, exactly right. 00:21:46.608 --> 00:21:48.350 You want to hide the Ace, because you 00:21:48.350 --> 00:21:49.527 want to go this way. 00:21:49.527 --> 00:21:52.110 And if you do it the other way around, it's not going to work. 00:21:52.110 --> 00:21:53.318 You're going to hide the Ace. 00:21:53.318 --> 00:21:58.050 And you're going to make the King the first card. 00:21:58.050 --> 00:22:02.780 And now, what you need to do is-- this is gone, right? 00:22:02.780 --> 00:22:05.210 And now what I need to do is, I need 00:22:05.210 --> 00:22:10.760 to encode a number between 1 and 6, in general. 00:22:10.760 --> 00:22:14.480 In this case, I need to encode the number 1 in order 00:22:14.480 --> 00:22:19.430 to give away the fact that the hidden card is an ace. 00:22:19.430 --> 00:22:23.310 And now I could do what was suggested before, 00:22:23.310 --> 00:22:25.670 which is have some sort of-- 00:22:25.670 --> 00:22:27.830 I mean, there's obviously an ordering 00:22:27.830 --> 00:22:32.000 associated with these cards that you see up here. 00:22:32.000 --> 00:22:34.940 If I call this a 1 and I call this a 13, 00:22:34.940 --> 00:22:37.850 then lets do the logical thing, which 00:22:37.850 --> 00:22:40.880 is, 1 is smaller than 2, which is smaller than 13, 00:22:40.880 --> 00:22:42.200 but I might end up-- 00:22:42.200 --> 00:22:44.750 I might have and Nine of Hearts here 00:22:44.750 --> 00:22:46.490 rather than a Five of Hearts. 00:22:46.490 --> 00:22:50.750 And I got to, obviously, be able to order the Nine of Hearts 00:22:50.750 --> 00:22:54.110 in relation to the Five of Hearts as well, so-- 00:22:54.110 --> 00:22:56.900 because I-- all of these could be nines actually, right? 00:22:56.900 --> 00:23:01.790 And so I can't just rely on the number to do the ordering, 00:23:01.790 --> 00:23:04.670 so I can just choose an arbitrary-- 00:23:04.670 --> 00:23:09.200 clubs is smallest. 00:23:09.200 --> 00:23:12.980 Diamonds is the next. 00:23:12.980 --> 00:23:15.680 And then I got Hearts. 00:23:15.680 --> 00:23:18.560 I just did this because this is a little bit 00:23:18.560 --> 00:23:20.570 easy to remember for me. 00:23:20.570 --> 00:23:22.550 You can do this in many different ways, 00:23:22.550 --> 00:23:26.960 in alphabetical order, you know, C-D-H-S. 00:23:26.960 --> 00:23:30.410 And so this-- that's moot here. 00:23:30.410 --> 00:23:33.810 What I need to do is to encode the number one, OK? 00:23:33.810 --> 00:23:36.440 But I encoded-- in order to encode the number one, 00:23:36.440 --> 00:23:39.320 I have to have some sort of way of ordering this. 00:23:39.320 --> 00:23:44.250 And so what I'm going to do is, I'm going to say SLM is one. 00:23:44.250 --> 00:23:46.460 So what do I mean by SLM? 00:23:46.460 --> 00:23:51.740 The smallest card is first-- 00:23:51.740 --> 00:23:55.390 I'm sorry, SML is-- 00:23:55.390 --> 00:23:58.170 increasing. 00:23:58.170 --> 00:24:01.320 The smallest card is the first one. 00:24:01.320 --> 00:24:03.670 The medium card is the second one. 00:24:03.670 --> 00:24:06.960 And the largest card is the third one, OK? 00:24:06.960 --> 00:24:08.800 And I'll write this out. 00:24:08.800 --> 00:24:10.390 And you can see the code for it. 00:24:10.390 --> 00:24:15.300 But when you see something like LMS, you're going to get a six. 00:24:15.300 --> 00:24:18.010 And there's obviously six of these different combinations, 00:24:18.010 --> 00:24:18.840 right? 00:24:18.840 --> 00:24:21.340 The details are actually entirely up to you. 00:24:21.340 --> 00:24:23.040 I mean, the most important thing here 00:24:23.040 --> 00:24:27.210 is the ordering that Billy had had to be ordering that I had. 00:24:27.210 --> 00:24:28.710 And so yesterday when we practiced, 00:24:28.710 --> 00:24:30.690 one time, there was a mismatch. 00:24:30.690 --> 00:24:32.040 And we got it wrong. 00:24:32.040 --> 00:24:36.090 But that's the only way the trick would fail, 00:24:36.090 --> 00:24:39.250 really, I mean, other than human error, is if the-- 00:24:39.250 --> 00:24:40.680 is the encoding. 00:24:40.680 --> 00:24:43.110 This is really encoding followed by decoding. 00:24:43.110 --> 00:24:47.950 And obviously, you need the same algorithm, if you will, 00:24:47.950 --> 00:24:52.290 which requires that you need the same ordering, in this case, 00:24:52.290 --> 00:24:53.990 for the cards, right? 00:24:53.990 --> 00:24:55.200 So that's it. 00:24:55.200 --> 00:24:57.710 That's the trick. 00:24:57.710 --> 00:25:00.900 It doesn't seem that interesting anymore, huh? 00:25:00.900 --> 00:25:03.570 But no, it is interesting if you show it to people. 00:25:03.570 --> 00:25:07.570 And the fun part is in actually doing it. 00:25:07.570 --> 00:25:10.570 So I encourage you all to do it. 00:25:10.570 --> 00:25:12.730 Any questions about how this trick works? 00:25:15.380 --> 00:25:20.740 So what I'd like to do is show you some code for this trick. 00:25:20.740 --> 00:25:25.150 And there's also a code that was useful to both of us, 00:25:25.150 --> 00:25:27.087 because we could practice by ourselves. 00:25:27.087 --> 00:25:29.170 We didn't have to be in the same room to practice, 00:25:29.170 --> 00:25:32.830 because I could randomly generate a bunch of these four 00:25:32.830 --> 00:25:33.400 cards. 00:25:33.400 --> 00:25:36.070 And obviously, the program knew what the hidden card was. 00:25:36.070 --> 00:25:36.930 And I could-- 00:25:36.930 --> 00:25:38.022 I'll show you the code. 00:25:38.022 --> 00:25:39.730 I could type in what the hidden card was. 00:25:39.730 --> 00:25:41.980 And it would say-- you know, I guess it would say, 00:25:41.980 --> 00:25:45.280 you're a mind reader extraordinaire, or sorry, 00:25:45.280 --> 00:25:46.330 not impressed. 00:25:46.330 --> 00:25:47.920 And Billy could do the same thing 00:25:47.920 --> 00:25:50.740 in terms of checking his encoding, all right? 00:25:50.740 --> 00:25:54.510 And then, after we're done here talking about the code-- 00:25:54.510 --> 00:25:58.060 and there are some interesting things with the code-- 00:25:58.060 --> 00:26:00.809 let's talk about whether you could-- 00:26:00.809 --> 00:26:02.350 talk about different kinds of tricks. 00:26:02.350 --> 00:26:03.975 And in particular, I want to talk about 00:26:03.975 --> 00:26:05.710 whether we could go from five cards 00:26:05.710 --> 00:26:11.310 to four cards using a different encoding scheme. 00:26:11.310 --> 00:26:19.700 Cool, so I wrote this code about a year ago. 00:26:19.700 --> 00:26:24.760 And I think I'd probably write it differently now, 00:26:24.760 --> 00:26:28.440 but we have what we have. 00:26:28.440 --> 00:26:34.590 So the first thing is you have to decide on an order. 00:26:34.590 --> 00:26:36.360 You absolutely have to decide an order. 00:26:36.360 --> 00:26:41.190 And the cards themselves, as I mentioned, 00:26:41.190 --> 00:26:44.650 there's a natural order associated with the numbers. 00:26:44.650 --> 00:26:48.810 And of course, you can decide if you want to start with a two, 00:26:48.810 --> 00:26:51.660 and then the ace could be 14-- 00:26:51.660 --> 00:26:54.822 I mean, kind of makes sense for you to go 1 through 13. 00:26:54.822 --> 00:26:56.280 So that's really what we have here. 00:26:56.280 --> 00:26:57.690 The ace is the smallest card. 00:26:57.690 --> 00:26:59.580 And the King is the biggest card. 00:26:59.580 --> 00:27:03.000 And as I mentioned, the clubs are smaller 00:27:03.000 --> 00:27:04.500 than the diamonds, et cetera. 00:27:04.500 --> 00:27:07.500 So I just have a deck of cards that 00:27:07.500 --> 00:27:09.570 is ordered as you see up there. 00:27:09.570 --> 00:27:11.370 And that's just a Python list that 00:27:11.370 --> 00:27:13.886 tells you what the ordering of these 52 cards are. 00:27:13.886 --> 00:27:14.760 Does that make sense? 00:27:18.580 --> 00:27:24.910 So there's many procedures here, many routines 00:27:24.910 --> 00:27:26.260 that do different things. 00:27:26.260 --> 00:27:27.890 And a lot of them use the same code, 00:27:27.890 --> 00:27:30.200 so I'm not going explain each one of them. 00:27:30.200 --> 00:27:32.270 But this one is a good one. 00:27:32.270 --> 00:27:35.260 And I'll also show you the computer assistant 00:27:35.260 --> 00:27:39.730 one, which is essentially this procedure except that it 00:27:39.730 --> 00:27:40.460 allows-- 00:27:40.460 --> 00:27:44.950 allowed me to practice by myself and generated cards randomly. 00:27:44.950 --> 00:27:48.940 In this case, what happens is, you input five cards. 00:27:48.940 --> 00:27:51.040 And what this does is-- 00:27:51.040 --> 00:27:53.800 so you could sort of take five cards out from the deck. 00:27:53.800 --> 00:27:58.360 And then manually, you can choose the hidden card, 00:27:58.360 --> 00:28:00.190 order the remaining four. 00:28:00.190 --> 00:28:02.740 And if you typed in those five cards 00:28:02.740 --> 00:28:05.110 into this particular procedure, it 00:28:05.110 --> 00:28:07.210 would give you the first four cards, OK? 00:28:07.210 --> 00:28:10.096 And so you can then verify that you've done the ordering. 00:28:10.096 --> 00:28:11.470 So this would be something that-- 00:28:11.470 --> 00:28:14.095 I don't know if Billy used this to practice, but he could have. 00:28:16.050 --> 00:28:17.920 So what do I have here? 00:28:17.920 --> 00:28:20.730 Well, the first thing is just printing out what the order is. 00:28:20.730 --> 00:28:23.580 There's a bunch of things that need to get initialized. 00:28:23.580 --> 00:28:28.830 Cards is simply a list of five cards. 00:28:28.830 --> 00:28:31.800 And then you have c index, or cind, 00:28:31.800 --> 00:28:35.670 which is the indices in that giant list 00:28:35.670 --> 00:28:39.004 that we have that had 52 cards in it. 00:28:39.004 --> 00:28:40.920 They're just the indices of the various cards. 00:28:40.920 --> 00:28:46.740 You can use .index, which is a method to go from a card, 00:28:46.740 --> 00:28:51.480 which is like a_c, for example, to the index. 00:28:51.480 --> 00:28:54.900 And then card suits are what suits are for the cards. 00:28:54.900 --> 00:28:58.830 And it's 0, 1, 2, and 3 for clubs, diamonds, et cetera. 00:28:58.830 --> 00:29:01.440 And then the numbers are what the numbers of the cards 00:29:01.440 --> 00:29:03.480 are, 1 through 13, OK? 00:29:03.480 --> 00:29:04.340 You kind of need-- 00:29:04.340 --> 00:29:05.631 there's a bunch of bookkeeping. 00:29:05.631 --> 00:29:08.820 As you can imagine, we're doing things in our head here, 00:29:08.820 --> 00:29:11.430 but if you want to get a computer program to actually do 00:29:11.430 --> 00:29:14.440 all of these computations, it's not complicated, 00:29:14.440 --> 00:29:16.380 but you have to worry about the four suits. 00:29:16.380 --> 00:29:18.330 And you've got to worry about the 13 cards. 00:29:18.330 --> 00:29:22.320 And you have to go ahead and encode SML, or produce 00:29:22.320 --> 00:29:23.280 this encoding, right? 00:29:23.280 --> 00:29:25.071 So you can imagine there's a bunch of code. 00:29:25.071 --> 00:29:28.951 It's not complicated code, but there's a bunch of code. 00:29:28.951 --> 00:29:30.450 So the first thing that happens here 00:29:30.450 --> 00:29:34.170 is, in this particular procedure, 00:29:34.170 --> 00:29:36.467 you want to input put these cards in. 00:29:36.467 --> 00:29:37.550 And so let me just run it. 00:29:37.550 --> 00:29:41.530 And so you get a sense of what this procedure does. 00:29:41.530 --> 00:29:42.810 All right, beautiful. 00:29:42.810 --> 00:29:45.360 So let's just say-- 00:29:45.360 --> 00:29:48.880 let me just pick five of these here. 00:29:48.880 --> 00:29:51.860 So the first one is Five of Hearts-- 00:29:51.860 --> 00:29:55.620 I'm sorry, Five of Hearts, yup, Five of Hearts, 00:29:55.620 --> 00:30:06.296 Nine of Diamonds, Jack of Spades, Ten of Hearts, 00:30:06.296 --> 00:30:07.990 Eight of Hearts. 00:30:07.990 --> 00:30:12.540 And so it essentially says the first-- 00:30:12.540 --> 00:30:14.380 so if I have something like this, 00:30:14.380 --> 00:30:23.990 it ended up choosing the Ten as the hidden card, 00:30:23.990 --> 00:30:28.520 and decided to choose Five as the first one. 00:30:28.520 --> 00:30:30.920 And then because Ten was the hidden card, 00:30:30.920 --> 00:30:33.470 you needed to encode 5, right? 00:30:33.470 --> 00:30:43.910 And so the way you encode 5 is by encoding L S and M. 00:30:43.910 --> 00:30:49.520 So the first card that should be up 00:30:49.520 --> 00:30:53.990 is a Jack, followed by the smallest card, 00:30:53.990 --> 00:30:56.760 which is an Eight, followed by a Nine. 00:30:56.760 --> 00:30:58.770 So that's essentially it. 00:30:58.770 --> 00:31:01.649 So now that you've seen that, let's take a look. 00:31:01.649 --> 00:31:03.815 I'm not going to go through every line of code here, 00:31:03.815 --> 00:31:09.140 but I want to point out a couple of things that are interesting. 00:31:09.140 --> 00:31:13.070 This is simply filling in the data structures. 00:31:13.070 --> 00:31:14.719 The only thing that's interesting here, 00:31:14.719 --> 00:31:16.760 or the thing that's probably the most interesting 00:31:16.760 --> 00:31:18.620 here is what I've highlighted. 00:31:18.620 --> 00:31:24.020 This is a way of taking an element in a Python list 00:31:24.020 --> 00:31:25.680 and getting the index for it. 00:31:25.680 --> 00:31:27.620 And so that's essentially something that-- 00:31:27.620 --> 00:31:29.670 it's object-oriented programming. 00:31:29.670 --> 00:31:33.560 We probably want to get into that in this class, 00:31:33.560 --> 00:31:38.040 but you'll definitely see that in 009 and other classes. 00:31:38.040 --> 00:31:40.640 And essentially, what we have here, given the ordering, 00:31:40.640 --> 00:31:49.640 is the suits simply correspond to whatever the indexes mod 4. 00:31:49.640 --> 00:31:52.180 Because, as you can see from this, 00:31:52.180 --> 00:31:58.070 the clubs are-- this is 0, the index 0, and the club 00:31:58.070 --> 00:32:02.870 is index 0, 1, 2, 3, 4. 00:32:02.870 --> 00:32:05.590 So you're going to get mod of clubs 00:32:05.590 --> 00:32:07.730 is always going to be-- mod 4 of clubs 00:32:07.730 --> 00:32:08.880 is always going to be a 0. 00:32:08.880 --> 00:32:12.800 Mod 4 of diamonds is always going to be a 1, et cetera, 00:32:12.800 --> 00:32:14.850 so that's essentially what happens here. 00:32:14.850 --> 00:32:17.490 And the first thing I need to do is figure out 00:32:17.490 --> 00:32:21.020 two a card that have the same suit, because that's important, 00:32:21.020 --> 00:32:24.560 because that's going to determine what my first card is 00:32:24.560 --> 00:32:25.880 and what my hidden cards are. 00:32:25.880 --> 00:32:28.160 And that's what happens over here. 00:32:28.160 --> 00:32:30.730 And then once I have that, I need-- 00:32:30.730 --> 00:32:34.490 I've just got to split these five cards into two piles, one 00:32:34.490 --> 00:32:37.760 of which has the hidden and the first card in it, 00:32:37.760 --> 00:32:40.550 and the other pile has the three cards that correspond 00:32:40.550 --> 00:32:41.654 to the ordering in it. 00:32:41.654 --> 00:32:43.070 Obviously, the computations that I 00:32:43.070 --> 00:32:45.500 have to do for the first couple are 00:32:45.500 --> 00:32:49.250 quite different from the ones for the remaining three cards. 00:32:49.250 --> 00:32:50.380 In one case, it's ordering. 00:32:50.380 --> 00:32:52.160 In the other case, it's a comparison. 00:32:52.160 --> 00:32:54.794 And I do have to-- the most interesting remaining part 00:32:54.794 --> 00:32:56.210 of the code that I'm going to show 00:32:56.210 --> 00:33:00.110 you is the determination of what the hidden card is 00:33:00.110 --> 00:33:01.550 and what the first card is. 00:33:01.550 --> 00:33:03.090 And that's going require-- 00:33:03.090 --> 00:33:05.600 this is the part that actually took me the longest to code. 00:33:05.600 --> 00:33:07.370 I got it wrong a couple of times. 00:33:07.370 --> 00:33:08.905 It's going to require me-- 00:33:08.905 --> 00:33:10.840 it's five lines of code, but it's subtle. 00:33:10.840 --> 00:33:13.250 It's going to require me to kind of figure out 00:33:13.250 --> 00:33:17.510 whether it's a jack versus two, you know, or vice versa. 00:33:17.510 --> 00:33:19.790 And things get a little bit interesting. 00:33:19.790 --> 00:33:20.856 For example, if you had-- 00:33:23.360 --> 00:33:31.250 if it wasn't the Jack and the Two, the example I had here, 00:33:31.250 --> 00:33:33.160 so let's do this-- put the Jack and Two. 00:33:33.160 --> 00:33:36.580 Let's say I had a Three and a Ten, right? 00:33:36.580 --> 00:33:38.800 They're kind of the furthest apart. 00:33:38.800 --> 00:33:42.070 And you had to be kind of super careful here, because 3 to 10 00:33:42.070 --> 00:33:45.130 is obviously 7, which is too large, 00:33:45.130 --> 00:33:47.720 but you need to go 10 to 3, which is 6, right? 00:33:47.720 --> 00:33:49.840 So the things that are diametrically 00:33:49.840 --> 00:33:52.120 opposite to each other are usually 00:33:52.120 --> 00:33:55.570 the hardest when it comes to actually doing the trick, 00:33:55.570 --> 00:33:58.210 but it's also hard from a standpoint of coding. 00:33:58.210 --> 00:34:01.120 I had to get the mods right, and the subtraction, 00:34:01.120 --> 00:34:05.420 and in terms of what got subtracted from the other. 00:34:05.420 --> 00:34:07.540 So the rest of it is-- 00:34:07.540 --> 00:34:09.949 I just have high level descriptions. 00:34:09.949 --> 00:34:13.900 Obviously, the code for these individual subroutines 00:34:13.900 --> 00:34:17.260 is in the file as well, but this one determines what's hidden, 00:34:17.260 --> 00:34:20.320 what the other card is, and what the number that you 00:34:20.320 --> 00:34:21.370 need to encode is. 00:34:21.370 --> 00:34:24.610 So when you go do the split, and you have the two cards, 00:34:24.610 --> 00:34:27.317 you obviously need to decide which one goes first, 00:34:27.317 --> 00:34:28.150 which one is hidden. 00:34:28.150 --> 00:34:29.860 And you also get the number. 00:34:29.860 --> 00:34:32.250 And that number had better be between 1 and 6, 00:34:32.250 --> 00:34:35.510 otherwise this is not going to work. 00:34:35.510 --> 00:34:38.515 And then you remove the other-- 00:34:38.515 --> 00:34:44.739 the two cards hidden in other from the set of five cards. 00:34:44.739 --> 00:34:49.030 In order to actually do this SML, 00:34:49.030 --> 00:34:53.230 it was a little easier for me to sort these cards. 00:34:53.230 --> 00:34:56.080 And then, depending on the number and code, 00:34:56.080 --> 00:34:57.550 I'd change the order. 00:34:57.550 --> 00:35:00.430 Obviously, if I sort the cards, I'm going to get SML. 00:35:00.430 --> 00:35:03.670 And that may not be what I want, but it's easier 00:35:03.670 --> 00:35:06.100 to start with SML, saying, this is 00:35:06.100 --> 00:35:09.430 the order that gave me the number 1 as an encoding. 00:35:09.430 --> 00:35:12.310 What do I need to do in order to change that encoding to a 2, 00:35:12.310 --> 00:35:14.650 or 5, or a 6, or what have you? 00:35:14.650 --> 00:35:18.660 OK, and so that's what this outputNext3Cards does. 00:35:21.650 --> 00:35:23.961 This is what took me the longest to code. 00:35:23.961 --> 00:35:25.960 I mean, it was a few minutes, but the rest of it 00:35:25.960 --> 00:35:29.320 was pretty much busywork. 00:35:29.320 --> 00:35:31.340 There wasn't too much thinking. 00:35:31.340 --> 00:35:36.890 So this thing here, as you can see, the encode is done-- 00:35:36.890 --> 00:35:40.970 you don't need to worry too much about the list itself, 00:35:40.970 --> 00:35:42.350 and the indexing into it. 00:35:42.350 --> 00:35:47.540 The bottom line is I need to figure out this situation. 00:35:47.540 --> 00:35:49.990 And I need to subtract. 00:35:49.990 --> 00:35:54.670 And so when I see something that says 10 and a 3, 00:35:54.670 --> 00:35:57.160 I end up getting a 7. 00:35:57.160 --> 00:36:00.310 And then I know that I have to do a flip, OK? 00:36:00.310 --> 00:36:03.900 But it also may be the case that I might get something that-- 00:36:06.430 --> 00:36:12.280 the reason I need the mod 13 is partly because I might end up 00:36:12.280 --> 00:36:13.990 getting a negative number. 00:36:13.990 --> 00:36:18.190 So it's not clear that encode, take away the mod 13, 00:36:18.190 --> 00:36:20.410 is going to give me a positive number. 00:36:20.410 --> 00:36:26.200 I might be subtracting 9 from 2, so I end up getting a minus 7. 00:36:26.200 --> 00:36:27.670 So you don't know this. 00:36:27.670 --> 00:36:29.989 I mean, the program doesn't know which one is which. 00:36:29.989 --> 00:36:31.780 And it has to figure out which one is which 00:36:31.780 --> 00:36:33.150 and flip them together. 00:36:33.150 --> 00:36:36.770 So if there's any code that you want to look at carefully, 00:36:36.770 --> 00:36:38.470 it's this code. 00:36:38.470 --> 00:36:40.302 And it's just a matter of sort of going 00:36:40.302 --> 00:36:42.010 through the combinations and making sure. 00:36:42.010 --> 00:36:45.330 I know it works, but you need to convince yourself it works. 00:36:45.330 --> 00:36:47.625 So that's pretty much it. 00:36:47.625 --> 00:36:50.950 There's not much more to say here 00:36:50.950 --> 00:36:56.560 that wouldn't be obvious to you looking at it carefully, 00:36:56.560 --> 00:36:59.730 so I don't want to belabor the obvious. 00:36:59.730 --> 00:37:03.920 And outputNext3Cards is the part that I just described. 00:37:03.920 --> 00:37:07.210 You start with the default ordering, which encodes a 1. 00:37:07.210 --> 00:37:09.400 And then you need to do a little bit of flopping, 00:37:09.400 --> 00:37:12.130 if you want to encode a 3, for example. 00:37:12.130 --> 00:37:13.840 And if you want to encode a 3, then you'd 00:37:13.840 --> 00:37:15.280 change things around. 00:37:15.280 --> 00:37:17.480 And this is exactly what I described to you before. 00:37:17.480 --> 00:37:19.760 So this is actually fairly straightforward. 00:37:19.760 --> 00:37:21.880 If you have that table written in front of you, 00:37:21.880 --> 00:37:25.420 you just go off it and write that. 00:37:25.420 --> 00:37:28.660 Certainly if you change the algorithm, all of this 00:37:28.660 --> 00:37:30.270 would change quite dramatically. 00:37:30.270 --> 00:37:34.660 And there's an exercise which asks 00:37:34.660 --> 00:37:39.400 you to do that, which you could certainly try to do. 00:37:39.400 --> 00:37:42.940 I want to show you one other thing, which is interesting. 00:37:42.940 --> 00:37:47.780 And then I want to run this new subroutine. 00:37:47.780 --> 00:37:51.230 So what I have here is, I'm going 00:37:51.230 --> 00:37:53.260 to run-- oh, I've already run it. 00:37:53.260 --> 00:37:57.820 So I want to show you computer assistant. 00:37:57.820 --> 00:37:59.230 It was very useful to me. 00:38:04.036 --> 00:38:05.910 And this says, please give me a random number 00:38:05.910 --> 00:38:07.680 of at least six digits. 00:38:07.680 --> 00:38:12.000 So obviously, I don't want to know 00:38:12.000 --> 00:38:13.980 what the hidden card is if I want to practice 00:38:13.980 --> 00:38:16.790 in a legitimate way. 00:38:16.790 --> 00:38:18.510 So what I did was, I said, I'm going 00:38:18.510 --> 00:38:19.677 to have this sort of hokey-- 00:38:19.677 --> 00:38:20.759 I mean, it's really hokey. 00:38:20.759 --> 00:38:22.650 I'm going to have this hokey algorithm that's 00:38:22.650 --> 00:38:26.490 going to take this giant number that, I'm going to type in. 00:38:26.490 --> 00:38:28.890 And it's somehow going to take this giant number. 00:38:28.890 --> 00:38:34.020 And it's going to deterministically generate 00:38:34.020 --> 00:38:38.582 5 cards based on this giant number, 00:38:38.582 --> 00:38:40.290 but I didn't want to have an obvious way. 00:38:40.290 --> 00:38:45.296 I mean, I don't want to say the number 12345 00:38:45.296 --> 00:38:47.670 and then end up getting the first five cards in the deck, 00:38:47.670 --> 00:38:49.200 or something like that, because that would sort of give it 00:38:49.200 --> 00:38:50.040 away right. 00:38:50.040 --> 00:38:53.610 So I want to have some sort of obfuscated way of taking 00:38:53.610 --> 00:38:56.490 a giant number and generating something that 00:38:56.490 --> 00:38:59.310 was at least unpredictable to me in terms of the five cards 00:38:59.310 --> 00:39:00.960 that are generated. 00:39:00.960 --> 00:39:04.940 And so what I do is, if I type in a number, 00:39:04.940 --> 00:39:06.480 some random number. 00:39:06.480 --> 00:39:08.580 And at this point, I have no idea 00:39:08.580 --> 00:39:13.020 what the five cards that are going to be generated are. 00:39:13.020 --> 00:39:17.950 And this just tell me-- it does do the assistant order 00:39:17.950 --> 00:39:20.670 the cards functionality, so it does take those five 00:39:20.670 --> 00:39:25.590 cards, hides a card, and then exposes the four cards to me. 00:39:25.590 --> 00:39:27.330 And so I'd get different-- depending 00:39:27.330 --> 00:39:28.380 on what number I type. 00:39:28.380 --> 00:39:31.800 So the way I'd practice is I'd just sort of 00:39:31.800 --> 00:39:34.170 close my eyes and just type some random number. 00:39:34.170 --> 00:39:36.220 And then it would produce four cards for me. 00:39:36.220 --> 00:39:39.830 And notice that this is wonderful. 00:39:39.830 --> 00:39:41.550 Notice that there's a bug, right? 00:39:41.550 --> 00:39:43.980 This is exactly why I put this up. 00:39:43.980 --> 00:39:49.222 And wow what luck, so notice that this didn't work. 00:39:49.222 --> 00:39:50.430 You know, and that's the fix. 00:39:50.430 --> 00:39:51.690 That's an exercise. 00:39:51.690 --> 00:39:53.280 I'm not-- I kid you not. 00:39:53.280 --> 00:39:56.130 It's an exercise that's going to be 00:39:56.130 --> 00:39:59.970 up there, which is fix my hokey algorithm so it doesn't 00:39:59.970 --> 00:40:01.470 do this. 00:40:01.470 --> 00:40:03.990 And so what happened here was, I had a deterministic way. 00:40:03.990 --> 00:40:05.890 This wasn't a random number generator. 00:40:05.890 --> 00:40:07.920 The good way of doing this would have 00:40:07.920 --> 00:40:12.630 been to use Python's random number generator facility 00:40:12.630 --> 00:40:15.690 and not have me do anything, because obviously I 00:40:15.690 --> 00:40:20.000 attached something that turned into that, which is a deck that 00:40:20.000 --> 00:40:22.620 has two King of Hearts in it. 00:40:22.620 --> 00:40:26.610 And so my deterministic way, which was a convenient way 00:40:26.610 --> 00:40:28.320 because it's only four lines of code 00:40:28.320 --> 00:40:35.100 didn't need me to include the Python random library, 00:40:35.100 --> 00:40:37.830 et cetera, causes trouble. 00:40:37.830 --> 00:40:39.730 So this obviously won't work. 00:40:39.730 --> 00:40:41.257 So I'll just type something. 00:40:41.257 --> 00:40:43.090 And it's going to say, sorry, not impressed. 00:40:43.090 --> 00:40:48.750 OK, not impressed with my guess and not impressed with my code, 00:40:48.750 --> 00:40:49.875 so let me do this again. 00:40:54.880 --> 00:40:58.150 And so let me just do that. 00:40:58.150 --> 00:40:59.140 And now-- what? 00:41:01.920 --> 00:41:04.290 Is this-- this is ridiculous. 00:41:04.290 --> 00:41:07.949 I mean, does my code even work? 00:41:07.949 --> 00:41:09.490 I'm going to blame it on my computer. 00:41:09.490 --> 00:41:12.370 I told you my laptop is acting up. 00:41:12.370 --> 00:41:12.870 OK. 00:41:16.940 --> 00:41:25.110 1111222-- ah-- thank you, all right, so now I see this. 00:41:25.110 --> 00:41:29.500 And I say Seven of Clubs, so that's the first card. 00:41:29.500 --> 00:41:30.990 So clearly, it's a clubs. 00:41:30.990 --> 00:41:35.160 And then Ten, King and Six, so Ten is medium. 00:41:35.160 --> 00:41:36.870 So I got medium, large-- 00:41:36.870 --> 00:41:38.910 MLS, right? 00:41:38.910 --> 00:41:41.370 So MLS, is-- 00:41:41.370 --> 00:41:43.200 MLS would be 4, right? 00:41:43.200 --> 00:41:47.950 So 4 would give me the Jack of Clubs, right? 00:41:47.950 --> 00:41:50.020 There you go. 00:41:50.020 --> 00:41:52.150 So this worked, OK? 00:41:52.150 --> 00:41:54.120 But now I want to show-- you the last thing 00:41:54.120 --> 00:41:55.370 I'll do is show you this code. 00:41:55.370 --> 00:41:58.050 And you guys should absolutely fix this code. 00:41:58.050 --> 00:42:01.200 It is clear what your exercise is. 00:42:01.200 --> 00:42:02.280 Or you could-- 00:42:02.280 --> 00:42:07.590 I do want to talk about doing this with four cards. 00:42:07.590 --> 00:42:12.750 So, as note is that, this is the offending line of code, OK? 00:42:12.750 --> 00:42:16.830 So what I did was, I wanted to generate five, kind of, 00:42:16.830 --> 00:42:19.530 random-looking numbers out of this giant number 00:42:19.530 --> 00:42:20.910 that I typed in, right? 00:42:20.910 --> 00:42:22.000 And I got lazy. 00:42:22.000 --> 00:42:24.310 And I was tired of this puzzle by the time 00:42:24.310 --> 00:42:26.050 I ended up coding it. 00:42:26.050 --> 00:42:27.620 So I just said, you know, I want-- 00:42:27.620 --> 00:42:32.194 I don't want to include random.lib from Python. 00:42:32.194 --> 00:42:33.360 I'm just going to take this. 00:42:33.360 --> 00:42:37.350 And I'm going to do some sort of iterative computation, where 00:42:37.350 --> 00:42:42.900 I'm generating what I think are random numbers between 1 and 52 00:42:42.900 --> 00:42:44.700 from this giant number that I typed in. 00:42:44.700 --> 00:42:46.986 And I'm going to do this five times. 00:42:46.986 --> 00:42:48.360 And what happened, as you saw, is 00:42:48.360 --> 00:42:50.910 that I generated the same number twice a couple of times, right? 00:42:50.910 --> 00:42:52.743 And that's why, obviously, the trick doesn't 00:42:52.743 --> 00:42:54.005 work in that case, right? 00:42:54.005 --> 00:42:55.380 What was interesting was, the way 00:42:55.380 --> 00:42:57.930 I found this bug was not the obvious way that we just 00:42:57.930 --> 00:42:58.590 saw here. 00:42:58.590 --> 00:43:04.410 It was actually something where the hidden card 00:43:04.410 --> 00:43:08.280 was the same as one of the four cards that was exposed. 00:43:08.280 --> 00:43:09.570 And I didn't know that, right? 00:43:09.570 --> 00:43:11.690 So I'm like, what? 00:43:11.690 --> 00:43:13.350 Why am I not getting this right? 00:43:13.350 --> 00:43:14.939 It kept saying, sorry, not impressed. 00:43:14.939 --> 00:43:17.355 And what it meant was, it wasn't impressed with my coding, 00:43:17.355 --> 00:43:20.400 not with my deductive skills. 00:43:20.400 --> 00:43:22.980 So it took me a while to figure this out. 00:43:22.980 --> 00:43:25.470 And you can fix it. 00:43:25.470 --> 00:43:28.440 OK, so that's it. 00:43:28.440 --> 00:43:30.900 Any questions about the-- what we've talked about, 00:43:30.900 --> 00:43:31.930 the puzzle, or the code? 00:43:34.860 --> 00:43:37.470 OK, so in the five minutes that we have left, 00:43:37.470 --> 00:43:38.970 let's talk about whether there would 00:43:38.970 --> 00:43:41.790 be a trick which would be perhaps even more 00:43:41.790 --> 00:43:46.110 impressive where we would only use four cards. 00:43:46.110 --> 00:43:50.880 So it would only be four cards that the audience selects. 00:43:50.880 --> 00:43:53.070 And we would-- 00:43:53.070 --> 00:43:56.640 Billy, I guess, would show me three cards. 00:43:56.640 --> 00:44:01.290 And I'd have to guess the fourth. 00:44:01.290 --> 00:44:04.080 Would that be possible? 00:44:04.080 --> 00:44:07.050 I mean, the numbers really don't work right, 00:44:07.050 --> 00:44:12.005 because that fourth card could be one out of-- 00:44:12.005 --> 00:44:13.380 I guess, if you show three cards, 00:44:13.380 --> 00:44:15.510 one of the 49 different possibilities. 00:44:15.510 --> 00:44:18.330 And it would be pretty difficult, right? 00:44:18.330 --> 00:44:25.560 You could think about something where-- 00:44:25.560 --> 00:44:27.620 the only way I could come up with 00:44:27.620 --> 00:44:29.304 was-- it required much more encoding, 00:44:29.304 --> 00:44:30.720 but I was thinking about something 00:44:30.720 --> 00:44:35.430 like this, where let's say I have these four cards, right? 00:44:35.430 --> 00:44:37.410 And let's even take-- let's say that they're 00:44:37.410 --> 00:44:39.977 all of different suits, right, because that's possible. 00:44:39.977 --> 00:44:41.810 The other thing that happens when you have-- 00:44:41.810 --> 00:44:43.860 when you only have four cards is they 00:44:43.860 --> 00:44:45.747 all four could be of different suits, right? 00:44:45.747 --> 00:44:46.830 That's certainly possible. 00:44:58.125 --> 00:44:58.750 What do I want? 00:44:58.750 --> 00:44:59.375 I want a heart. 00:44:59.375 --> 00:45:02.410 OK, good, so I have something like this. 00:45:02.410 --> 00:45:04.764 And now I'm in real trouble. 00:45:04.764 --> 00:45:06.430 I mean, clearly, anything that we talked 00:45:06.430 --> 00:45:08.410 about isn't going to work. 00:45:08.410 --> 00:45:14.830 So let's just say that I end up choosing one of these cards 00:45:14.830 --> 00:45:15.730 to hide, right? 00:45:15.730 --> 00:45:19.240 So this Ace is hidden, because it's not 00:45:19.240 --> 00:45:22.480 quite clear what I can do here, but bear 00:45:22.480 --> 00:45:24.590 with me for just a minute. 00:45:24.590 --> 00:45:28.390 So for argument's sake, let's say that now, at this point, 00:45:28.390 --> 00:45:31.240 I'm trying to get more information out of this. 00:45:31.240 --> 00:45:32.840 The ordering isn't going to help me. 00:45:32.840 --> 00:45:35.770 I mean, the ordering is going to help me a little bit, but what 00:45:35.770 --> 00:45:37.450 am I going to get, like 6-- 00:45:37.450 --> 00:45:40.030 1 through 6 from this? 00:45:40.030 --> 00:45:44.980 So I could say the first card is an anchor, OK? 00:45:44.980 --> 00:45:47.620 And so I'm going to expose this. 00:45:47.620 --> 00:45:51.002 So the only thing I could think of was, you could sort of do-- 00:45:51.002 --> 00:45:52.210 this is a little bit obvious. 00:45:52.210 --> 00:45:53.680 And I'm maybe giving things away. 00:45:53.680 --> 00:45:56.950 But depending on where you have the hidden card, 00:45:56.950 --> 00:46:01.660 and you can get more information based on the order 00:46:01.660 --> 00:46:04.510 in which you put these cards out and whether they're 00:46:04.510 --> 00:46:08.500 to the left or the right of this hidden card. 00:46:08.500 --> 00:46:10.210 So you'd need to do something like that. 00:46:10.210 --> 00:46:13.120 I mean, I haven't figured this out. 00:46:13.120 --> 00:46:18.970 At least, I can't think of a complete solution 00:46:18.970 --> 00:46:22.720 to this puzzle, but I do feel like that you 00:46:22.720 --> 00:46:26.110 can get some information, additional information based 00:46:26.110 --> 00:46:28.910 on whether you put things to the left or the right. 00:46:28.910 --> 00:46:31.780 And that's clearly a bit of information that you get. 00:46:31.780 --> 00:46:33.520 And maybe you could add to that. 00:46:33.520 --> 00:46:36.050 And you know, think about it. 00:46:36.050 --> 00:46:38.896 I think it makes for an interesting exercise. 00:46:38.896 --> 00:46:40.270 And obviously, there's other ways 00:46:40.270 --> 00:46:43.650 of doing the five-card trick, as well. 00:46:43.650 --> 00:46:46.690 Cool, all right, that's all I had for today. 00:46:46.690 --> 00:46:49.060 If there are no questions, we can 00:46:49.060 --> 00:46:51.620 close this particular session.