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Programming Enigma Puzzles

17 February 2017

Posted by on **From New Scientist #1533, 6th November 1986** [link]

Our local club’s darts’ champion Rice Robswit was about to throw three darts in an attempt to win the match. The score he needed could have been got with one treble, but in order to show his prowess and to finish with a double he went for a single, a treble of a different number, and a double of a different number again (avoiding the bulls) in order to give him exactly the total he wanted. Being an experienced player he did not actually look at the numbers around the board — he simply threw the three darts into exactly the positions he had planned.

The crowd roared their approval until someone pointed out that, after the board had fallen on the floor at the end of the previous player’s throw, it had been hung up upside down. There was a groan from the crowd until, on a fresh and proper count, it was found that Rice had

stillscored his correct required total.What was that total?

(The numbers around a darts board are in the order 20, 1, 18, 4, 13, 6, 10, 15, 2, 17, 3, 19, 7, 16, 8, 11, 14, 9, 12, 5, 20, …).

[enigma384]

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This Python program runs in 43ms.

Solution:The total was 54.The total can be made as:

54 = 6 + 2× 12 + 3× 8

or:

54 = 11 + 2× 2 + 3× 13

where (6, 11), (12, 2) and (8, 13) are diametrically opposite scores.

Of course we don’t know whether he want for (single 6, treble 8, double 12) and accidentally got (single 11, treble 13, double 2) or vice versa. I would tend to think you would aim to finish on the double 12, so that if you missed and got a single 12 on your next go you could try for a double 6 (and if you missed that and got a single 6 you could then try for double 3).