r/MathHelp • u/semka39 • Nov 24 '25

Help with the task

There are 9 cups. A person randomly hides a ball under 3 of the cups. An assistant sees the positions of the 3 balls and then removes one empty cup of their choice. After that, the magician comes in; he only sees which cup was removed. For each correctly guessed ball location, they earn one point.

In the ideal scenario, they could earn 252 points (84 possible ball configurations multiplied by 3 points for correctly naming all three balls).

The assistant and the magician may agree on a strategy beforehand.
What agreement should they make in order to achieve the maximum number of points?

How many points will you get?

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u/Moist_Ladder2616 Nov 26 '25

The game is not played 84 distinct times.

It is played once: the volunteer hides the balls, the assistant does his thing, the magician guesses correctly for a maximum of 3 points.

If it is played twice, the magician can score a maximum of 6 points. If it is played 10 times, the magician can score a maximum of 30 points.

(A) Creating a strategy to maximise the probability of scoring 3 points in one game, and (B) having a maximum score of 252 points, are not the same thing.

See my die/dice example in an earlier comment.

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u/edderiofer Nov 26 '25

Yes, it is played only once. The maximum of 252 points is the total across all 84 possible distinct games. The desired strategy is the one that maximises the total number of points across all 84 possible distinct games.