Fifteen is the goal
Satvik and Agnishom are playing a game. There are a set of nine Cards numbered from 1 to 9.
The two take turns to select and pick up a numbered card of their choice. Satvik goes first, picks up a card, then Agnishom picks a remaining card and so on.
The first player to make a set of 3 cards that sums up to 15 wins the game.
Assuming optimal strategy by both the players, what is the percentage probability that this game ends in a draw?
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1 solution
Discussions for this problem are now closed
Moderator note:
Fantastic solution!
Optimal strategy for Satvik and Agnishom is to mentally arrange the numbers 1 to 9 in a 3 by 3 magic square where each row, column and diagonal adds up to 15. Now the player getting to 15 first is the same as getting 3 in a row first on the magic square.
8 1 6
3 5 7
4 9 2
This is exactly like the game of tic-tac-toe. Since with optimal strategy, tic-tac-toe always ends in a draw, the probability that this game ends in a draw is 100 %.