Player is to be identified
Three players A, B and C are playing a game with three cards : on each card a positive integer is printed. The three printed numbers are supposed to be distinct. A game consists to mix up the cards, to distribute one card to each player and then to assign to the player the number printed on his card. The next game proceeds in the same way and the points are added. After a number of games, at least two games, player A has 20 points, player B has 10 points and player C has 9 points. It is known that the player B has the greatest card in last game.
Which of these players did have the middle card in the first game?
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1 solution
Let S represent the smallest card, M represent the middle card, and L represent the largest card. ∣ ∣ means 'or'.
In B's scenario, his last card is L , but he ends up with the middle amount of points, meaning he must have had S in the beginning.
S + L = 1 0
In A's scenario, he ended up with the largest number of points, so he must have started with the largest card or medium card in the beginning, and ended with the largest or medium card.
( L ∣ ∣ M ) + ( M ∣ ∣ L )
In C's scenario, he ends up with the least amount of points, meaning that he must have had M , and then got S .
M + S = 9
We can modify A's scenario to L + M = 2 0
Anyways, C had M .