Enigma 1083: Trios of semi-primes
18 December 2017
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From New Scientist #2239, 20th May 2000 [link]
A semi-prime is the product of two prime numbers. Harry, Tom and I each chose a set of three two-digit semi-primes which formed an arithmetic progression, such that the six factors of the three semi-primes in any one set were all different. The first (lowest) number in each of our sets was identical.
We then each chose another such set. This time the middle number in each of our sets was identical.
We then each chose another such set. This time the last (highest) number in each of our sets was identical, and of the other two semi-primes in my set one also appeared in Harry’s set and the other also appeared in Tom’s set.
The nine sets that we chose between us were all different, but one semi-prime appeared in all three sets that I chose.
List the three sets that I chose in the order in which I chose them, with the numbers in each set in ascending order.