**From New Scientist #2473, 13th November 2004**

Messrs Archer and Bowman each fired three arrows. The arrows recorded six different scores between 2 and 10.

The cumulative score of each of them at any stage was always a prime number. Archer had the greater cumulative score after each had fired one arrow and again after each had fired three arrows, Bowman had the greater cumulative score after each had fired two arrows.

What did Bowman score with each of his arrows? Give the scores in the order in which they were recorded.

When I did archery I was told you couldn’t “fire” an arrow, as there was no fire involved. So, we used to “shoot” arrows.

[enigma1315]

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This recursive Python program solves the problem in 37ms.

Solution:Bowman’s scores (in order) are 3 points, 10 points, 4 points.Archer’s scores (in order) are 5 points, 6 points, 8 points.