Enigma 972: Fifty-fifty
21 February 2020
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From New Scientist #2127, 28th March 1998
Bunko, Jack and Patience have a pack of cards that consists of fewer than one hundred cards which are numbered consecutively: 1, 2, 3, 4, 5, 6, …
On one occasion recently they were each given one of the cards (without the other two players seeing which).
Bunko said: “There’s an exactly 50:50 chance that my card is the highest of our three”.
Then Jack added: “In that case there’s an exactly 50:50 chance that, in decreasing order, the cards are Bunko’s, Patience’s then mine”.
How many cards are there in the pack? And what was Jack’s card?