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Programming Enigma Puzzles

20 December 2021

Posted by on **From New Scientist #2093, 2nd August 1997**

Harry, Tom and I were trying to find sets of three two-digit prime numbers such that if we added any two numbers of the set together the answer was double a prime. Within each set the three prime numbers had to be different; but we each found that having created a set we could created a second set by changing just one number in our first set.

One of my two sets was the same as one of Harry’s sets and the other was the same as one of Tom’s; their other sets were different.

(1) What were my two sets?

(2) Which set might we have found whose three primes do not appear in any other set?

I don’t have a source image for the puzzle as originally published, but I believe the above text is correct.

[enigma938]

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This Python program runs in 56ms.

Run:[ @replit ]Solution:(1) The setters sets were (11, 23, 71) and (11, 23, 83); (2) The set disjoint from all others is (13, 61, 73).A programme/manual solution.

I defined a function for a primality test for three numbers – if the sum of any two (from three) primes, divisible by two, was prime. There were only seven groups of three primes, of which five were used in the answers.

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