The equation below involves four 5-digits prime numbers:

A + B + C = D

A, B and C are consecutives, B and D are palindromes.

Find A, B, C and D.

(In reply to Analytical Solution, Part 2 by Sir Percivale)

Well I had to resort to trial and error at this stage but was happy to find I only had to check the first two before hitting on the answer as B=10501 leads to the full solution:

10499+10501+10513=31513

I see now why pcbouhid wanted an analytical solution so much;

in part one I was able to rule out all but 94 of the 90,000 five digit numbers,

in part two I got it down to 35 possibilities,

then, I only had to rule out one more possibility before arriving at the answer. A very satisfying exercise in solution by elimination, from 90,000 possibilities to 1, in 6 logical steps.

I used to think computer solutions were not a problem because I just ignored them. Have to say that I would have assumed this problem was beyond me after seeing a scholar had resorted to using a computer to solve. I only attempted it in tribute to pcb. Great puzzle, thankyou.

Posted by Percy on 2006-01-18 14:58:50