Puzzle Time
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Yes that should work.
A conceptually similar solution that is easier to compute in your head in ‘magic trick time’:
Based in Ax’s observation that there is always at least one suit with two cards within the 5.
George chooses one of the two cards of the same suit, puts the other on top of the four he hands to Cats.
With the other three cards he can communicate a number between 1-6. He use that number to indicate how much higher the reserved card is than the top card, allowing for the cycle from K->A->2.
Example. He puts the queen of clubs on top with the reserved card being the 5. He indicates 6 with the other three cards. Cats knows that from Q you count K,A,2,3,4,5 so the reserved card is a 5.
What if the reserved card was a six? In that case George would have reserved the Q and handed Cats the 6 on top of the deck, still indicating 6 with the other three cards. (7,8,9,10,J,Q). In other words, by strategically choosing between the two cards of that suit, the additional 3 cards can convey enough information.
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Yeah that's conceptually identical but for the range being 1-13 rather than 1-52. But with some practice I don't think either is particularly difficult to compute in magic trick time. To identify the number between 0 and 23 based on the order of 4 cards, let hte first card indicate which quartile the number is in, then the second card indicate which tri-cile of that, and the third card which of the two remaining numbers it is.
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Mostly from a mailing list from a university ‘math circle‘ we were involved with in NC
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Today it is my responsibility to present a game during a department zoom meeting that we can all participate in. I'm going to give them this puzzle, but I'll have them try to solve it as a group rather than individually and competitively. Should be fun. Maybe I'll be surprised and they'll come up with a solution quickly.
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Cool. make sure you say 'copyright jon-nyc 2020'.
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I've since learned that this very method (using top card as suit indicator and three cards as identifier) was used by a magician from the 30s. Probably invented by him.
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William Fitch Cheney, was his name. Apparently a mathematician and magician.
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@Horace said in Puzzle Time:
Today it is my responsibility to present a game during a department zoom meeting that we can all participate in. I'm going to give them this puzzle, but I'll have them try to solve it as a group rather than individually and competitively. Should be fun. Maybe I'll be surprised and they'll come up with a solution quickly.
How'd it go?
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There was a surprise guest and thus no game-time during that meeting. Then the following week there was again no game time. I suppose I'll be on the hook but only if we ever do another game time. Nobody likes these game times during these meetings, but games are fun, and even if nobody has any fun, they are still fun. Just ask everybody professionally obligated to attend the zoom meeting.