Two 2-digit numbers add up to a third 2-digit number. Each of the three numbers is the product of two primes. Each of the six primes is different.

If you take the two addends and combine the tens digit of one with the units digit of the other, and vice versa, they will of course add up to the same 2-digit number as before. But in addition, for these chosen numbers, the two mixed numbers (the new addends) are each also the product of two primes, and these six primes also are all different, but may contain repeats from the first set of six.

What are the numbers involved?

using mathematica I found the following solution

35=7*5 58=2*29 35+58=93=3*31 primes 2,3,5,7,29,31
38+55=93 and 38=2*19 and 55=5*11 and the second set of
primes are 2,3,5,11,19,31

now of course the reverse of this starting with 38 and 55 also gives a valid solution,  so the 5 numbers in reference are 35,58,38,55 and 93

Posted by Daniel on 2009-05-24 15:08:38