Three 3-digit primes, all digits being distinct, sum up to a three digit number.

Can you find this number?

Please provide answers to two distinct versions of the problem:

a. No zeroes allowed .

b. Zeroes, non-leading of course, can appear on both sides of the equation.

(In reply to

re: No Subject by Ady TZIDON)

The sum 999 is possible with numbers being 149, 263 and 587.

If there is a single sol. then i guess the case with sum 909 is not possible. but its becoming too dificult to check !

The case with zeroes allowed introduces further problems which make other complications. Zeroes can only be in the middle place. As in the end they wont make a prime and in the start they wont make a three digit number.

The first digits still have to be 1,2,4 or 1,2,5.

Also last digit of the 3 numbers have to be 3, 7 and 9. Hence the sum of the three primes also has last digit 9.

*Edited on ***September 19, 2010, 6:08 pm**