A Nim Variant

You are going to play a game with your friend. You and your friend will alternate picking numbers from 1 to 6 and a running total will be kept. The object is to be the player who makes the total exactly 50. You insist on going first. What number should you pick first to guarantee yourself the win?

Scroll down for a clue and further down for the answer.

*

*

*

*

*

*

*

Clue: After the first turn, you will pick 7 minus the number that your opponent picks.

Scroll down for the answer.

*

*

*

*

*

*

*

Answer: You should pick the number 1.

As 50 is 1 more than a multiple of 7, you should pick the number 1 on your first turn. After your first turn, regardless of what number your opponent chooses, you will pick 7 minus that number. This means on your eighth turn, you will be able to reach 50.  

* This article was originally published here