Here’s an interesting question recently posed by my friend Lee.
Imagine there is a theoretical game:
There are 9 cards, numbered 1-9, lying face up on a table in front of two players. Each player takes turns picking up one card from the table. A player wins if they collect any three cards whose numbers sum up to 15. The game ends in a draw if all 9 cards are picked up without either player achieving any combination of three cards satisfying the above. Is there a winning strategy?
Lets start out by looking at the winning state. You need a combination of three numbers and this combination must sum up to 15. There are eight combinations of numbers 1-9 (inclusive) that sum up to 15.
Now for the cool part. After a hint from a friend I realized that the numbers can be formed into a magic square like this:
There are eight combinations of numbers 1-9 that sum up to 15, as shown by the magic square. From here on the problem can be conceptualized as a game of tic-tac toe. However, we know that in tic-tac-toe there is no perfect winning strategy. Two players using the same winning strategy will always end up in a draw. Thus, there is no perfect winning strategy for our given game.