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The middle ham

The middle ham

The middle ham is a game for three people. The cards from 1 to 9 of one of the four suits of the deck are mixed and then three cards are distributed to each of the players. In secret, each one adds his three cards and wins the one that has the sum that is right in the middle.

In a game, a player receives his three cards and before his teammates show their scores he jumped for joy and exclaimed: I won!

What letters did you receive?

Solution

As the sum of 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45 divided by 3 people gives 15, the secret to ensuring the triumph of our friend is that he adds 15. In addition, it must be such a combination that does not allow draws so that the only possibilities are:

4-5-6 and 2-5-8
These two combinations do not allow the remaining numbers that the other players could have to add 15.

The other combinations that add up to 15 cannot be considered a priori winners because they could cause draws.

1-5-9 could cause triple draw if the second player is 3-4-8 and the third is 2-6-7. On the other hand, the 3-5-7 combination could tie with 2-4-9 and 1-6-8.