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Thrice three is nine (Posted on 2010-09-11) Difficulty: 3 of 5
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.

No Solution Yet Submitted by Ady TZIDON    
Rating: 4.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts Thoughts | Comment 2 of 5 |

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
  Posted by Vishal Gupta on 2010-09-14 16:38:26

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