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.

Posted by Vishal Gupta on 2010-09-14 16:56:52