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Programming Enigma Puzzles

29 November 2019

Posted by on **From New Scientist #2137, 6th June 1998** [link]

In a recent frame of snooker “Earthquake” Endry and “Polly” Parrot had a close contest.

Earthquake went first, and each time either player visited the table the number of balls potted was the same (and the same for both players). And each time Earthquake potted a red he followed it by attempting to pot one particular colour. And each time Polly potted a red he followed it by attempting to pot one particular colour.

Building up to a grand climax, Earthquake potted the pink but was still behind. He then potted the black to win.

That’s not enough information for you to be able to answer the following question, but if I told you whether or not two consecutive pots were ever the same colour then you would have enough information to answer the question.

What was the final score in points?

(Remember, in snooker there are 15 reds. The potting of a red earns one point and enables the player to try to pot one of the other six colours, earning from 2 to 7 points. A successful pot means that the player can try for another red, and so on. The reds stay down but the other colours are put back on the table. If an attempt to pot a ball fails then the other player has a turn at the table. When all 15 reds have gone and all 15 attempted pots at colours are completed, the six remaining colours are potted in order, and this time they too stay down. No other rules concern the frame described in this

Enigma).

[enigma982]

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This Python program runs in 100ms.

Run:[ @repl.it ]Solution:The final score was: Endry, 54 points; Parrot, 48 points.Each player potted 12 balls on each turn. Endry’s colour was yellow (2 points). Parrot’s colour was black (7 points).

The game proceeded as follows:

In

E‘s second go he pots two consecutive yellows (2 points).There are two scenarios where there are no consecutive pots of the same colour: