# 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