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.

Have some thoughts.

As far as i understand, the 9 digits used for the 3 3-digit numbers are distinct. So each of 1,2,3....9 is used once.

The three numbers are 3-digit primes so they have to be odd.

So last place can be 1,3,5,7,9. Also 5 is not possible in last place for number to be prime. So, 1,3,7,9 can be in the units places of the three numbers.

Also max digit in the hundred's place is 6 as the other two will be min of 1 and 2. One of the hundred's digit has to be from 1 or 3 as otherwise the smallest numbers with hundred's digit 2,4,5 will sum to a four digit number.

So, 7 and 9 are definitely two of the units digits. third unit place can be 1 or 3. So the number formed by adding these 3 numbers will have unit digit either 7 or 9.

*Edited on ***September 14, 2010, 4:41 pm**