Puzzle Time
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How would you do the encoding of the 48? What kind of prima facie coding scheme would you use when you don’t know in advance which 48 cards you’ll be distinguishing among?
Ax - you’re on the right track. Or a right track at least.
@jon-nyc said in Puzzle Time:
What kind of prima facie coding scheme would you use when you don’t know in advance which 48 cards you’ll be distinguishing among?
That part's easy.
From the 52 cards, subtract the 4 cards that were handed to Cats. Sort them. Name them 1 to 48.
The number encoding is: Name the 24 sorting orders s1 to s24. If you transmit 0 via the method I described above, sorting s-n stands for card n. If you transmit 1, it stands for 24+n.
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Considering 5 random distinct numbers from 1 to 52, the magician could choose either the highest or the lowest number to keep secret, while ordering the remaining four to identify a number between 1 and 24, since there are 24 orderings of four distinct things A,B,C, and D where A is the lowest number, B the second lowest, etc. The magician would choose either the highest or lowest of the 5 numbers, whichever one was within 24 of the remaining highest number, considering 52 to roll over to 1 as numbers increase. This should always be possible. The assistant would identify the hidden number as the indicated offset from the highest of their four cards, rolling over from 52 to 1 if necessary.
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Education is extremely important.
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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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Considering 5 random distinct numbers from 1 to 52, the magician could choose either the highest or the lowest number to keep secret, while ordering the remaining four to identify a number between 1 and 24, since there are 24 orderings of four distinct things A,B,C, and D where A is the lowest number, B the second lowest, etc. The magician would choose either the highest or lowest of the 5 numbers, whichever one was within 24 of the remaining highest number, considering 52 to roll over to 1 as numbers increase. This should always be possible. The assistant would identify the hidden number as the indicated offset from the highest of their four cards, rolling over from 52 to 1 if necessary.
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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.
Education is extremely important.
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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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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.
@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.
