Open In App
Related Articles

Puzzle 79 | Magical Matrix

Improve Article
Save Article
Like Article

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. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above

Whether you're preparing for your first job interview or aiming to upskill in this ever-evolving tech landscape, GeeksforGeeks Courses are your key to success. We provide top-quality content at affordable prices, all geared towards accelerating your growth in a time-bound manner. Join the millions we've already empowered, and we're here to do the same for you. Don't miss out - check it out now!

Last Updated : 18 Jan, 2023
Like Article
Save Article
Similar Reads