# Puzzle 79 | Magical Matrix

Last Updated : 18 Jan, 2023

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.

This puzzle is contributed by Ankur Chaudhary.

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