1.8 Induction

Unstacking Game Score

Suppose that there is a game that entails unstacking a tower of \(n \) blocks. A move entails splitting a stack of \(k \) blocks into two stacks of \(a \) and \(k-a \) blocks. Also define the score for a move to be the product of the number of blocks in the created substacks (e.g. \(k(a-k)\)). The overall score for the game is the sum of the scores accumulated over all the moves. Which of the following is true about the overall score?

Exercise 1