Sunday Times Teaser 2498 – No Title
by Victor Bryant
Published August 8 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?
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After three cards have been chosen, Victor chooses two cards from the three to give to Keith. There are six ways he can do this – three choices for the first card followed by two choices for the second. Each of these six choices can hence be used to identify one of the remaining six cards, which means that the trick will work for up to eight cards.
By passing the cards with a left or right hand on each of the two occasions, the number of possibilities is increased from six to twenty four. So, in addition to the two cards passed, a further twenty four cards can be identified so the trick will now work for up to twenty six cards.
Hence the final letter is Z.