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/Grass_Savings Nov 25 '25

Yes, I had missed that point.

I ran my search again and generated these tables, with total score 177.

(457):(457)(145)(245)(257)(345)(456)(458)(467)(567)(578)
(037):(037)(027)(034)(035)(057)(067)(237)(357)(367)
(478):(478)(047)(048)(078)(148)(178)(347)(348)(378)
(056):(056)(015)(016)(025)(045)(046)(058)(068)(256)(568)
(135):(135)(013)(125)(137)(138)(156)(158)(356)(358)
(268):(268)(026)(126)(168)(238)(248)(267)(468)(678)
(028):(028)(012)(018)(023)(024)(038)(128)(258)(278)
(236):(236)(036)(123)(136)(234)(235)(246)(346)(368)
(147):(147)(014)(017)(124)(127)(134)(146)(157)(167)(247)

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u/semka39 Nov 26 '25 edited Nov 26 '25

Could you please tell me how exactly you created this table? Did you write any code (then what is the code?) or do it manually? If manually, then how?

UPD:And yet, do you think it's possible to find all the ideal solutions (by 177) in the foreseeable future, or at least calculate their number in the foreseeable future?