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.

For 3 as hundred digit. 2,3 and 4 have to be hundred's digits.

They add up to 900. Units digit are 1,7,9 (sum=17). Ten's digit will be made up of 5,6,8 (sum=190). Total number will become 1107. SO not possible.

**So, last digits are 3,7,9 (sum=19).**

First digits can be 1,2,4 or 1,2,5 or 1,2,6

(i) 1,2,6 is not possible because of sum constraint.

(ii) 1,2,5 adds to 800. ten's place will be 4,6,8 (sum=180). unit's place 3,7,9 (sum=19). So number on adding is **999**.

(iii) 1,2,4 adds to 700. ten's place 5,6,8 (190).unit's place 3,7,9 (19). So number on adding is **909**.

Now problem is to see if primes can be made with above configurations. In any case the final number is **either 909 or 999**.