Two friends Satyam and Ankit decides to play a game. They have 9 cards lying face up with numbers 1 to 9 written on them. They have to start picking up these cards alternately, without replacement. The person with exactly 3 cards which adds up to 15 wins the game. Satyam is given first chance to pick up a card .

Does Satyam have a winning strategy?

Not Really

We can see that {1,9} has 8 subsets for a total of 15. these are:

{1, 5, 9}, {2, 8, 5}, {3, 5, 7}, {4, 5, 6}, {1, 6, 8}, {2, 4, 9}, {2 , 7, 6} and {3, 8, 4}

We can create a magic square that can derive all possible combinations that add up to 15.

8 1 6

3 5 7

4 9 2

Here we can see that every row, column or diagonal equals 15. These rows, columns and diagonals represent all possible ways to reach the number 15.

It turns out to be something like a tic-tac-toe game of magic squares. I also understand that there are no guarantees of winning in this game. At best, you can have a strategy for not losing the game.