Teaser 2498: [Party trick]
From The Sunday Times, 8th August 2010 [link]
Keith and I used to do a party trick. We had a set of cards labelled A, B, C, D, E, F, G and H. We would ask someone to choose three cards without Keith seeing. I would pass Keith one of the chosen cards, followed by a second. Amazingly, he would announce what the third chosen card was. Keith and I have phenomenal memories, so I then thought of a way to improve the trick. On each of the two occasions, I pass a card with either my left or right hand. Using this extra piece of trickery, we increased the number of cards in the set, ending with a letter way beyond H.
What is the letter on the last card?
This puzzle was originally published with no title.
[teaser2498]
S2T2 
Jim Randell 8:15 am on 21 November 2025 Permalink |
See also: Enigma 1214 (which was set by Keith Austin).
There are 3 cards chosen, so the setter has P(3, 2) = 6 ways they can choose to present two of the cards to Keith. If each of these ways is used to identify the remaining card there can be up to 6 + 2 = 8 cards in the pack. And this is the initial scenario.
In the second part of the puzzle each of the two passes can be made with the left (L) or right (R) hand, so each of the 6 ways of presenting the cards can have 4 variations (LL, LR, RL, RR), so there are now a total of 6 × 4 = 24 different ways of identifying the missing card. So there can be up to 26 cards in the pack. Hence:
Solution: The last card has the letter Z on it.
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