easy Brainteasers

Counting Game

A release-checked easy problem for training Brainteasers.

Question

You and a friend play a game in which they each take turns selecting a number. The first player starts by selecting a number from $1-8$. The second player then selects a number that is $1-8$ numbers higher. They continue this until one player selects $200$, in which case they win the game. Assuming both players play optimally, if you are the first player, what number do you select to always win the game?

Practice focus

This Brainteasers problem is tagged Brainteasers. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.