Mr. X and Mr. Y live in the same avenue with only 9 houses between them. The number on their houses were both prime, and Mr. X found that he could express the number of his house as the sum of the squares of the digits of Mr. y's house number.
What were their house numbers ?

assuming the larger number is two digits: n2=10a+b
we have n1=a²+b²
additionally we know that n2=n1+18 (9 houses apart on the odd side of the avenue).
then brute force search on primes for n2 from 11 to 97, yields:
n1=25
n2=43

Posted by Hanan Rosemarin on 2004-03-26 07:47:23