# Puzzle 79 | Magical Matrix

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?
Solution: No
Explanation: We see that there are eight subsets of {1,9} that sums up to 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 try to form a magic square which should be able to derive all possible combinations that sums up to 15.
8 1 6
3 5 7
4 9 2
Here we see each row , column or diagonals sums up to 15. These rows ,columns and diagonals represents all the possible ways the number fifteen can be arrived at.
We can observe it’s like playing a tic-tac-toe on the magic square. We also know one cannot guarantee winning in this game. At maximum, we can have strategy of not losing the game.