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Programming Enigma Puzzles

21 February 2020

Posted by on **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?

[enigma972]

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This Python program runs in 83ms.

Run:[ @repl.it ]Solution:There were 22 cards in the pack. Jack’s card was 5.Bunko’s statement can only be true if there are 22 cards in the pack, and he was dealt card 16.