Question

Andre makes a three-digit number.

All the digits are odd.
The sum of the digits is 7.
What could Andre's number be?

Answer 1

Answer: 115,151,115,133,313,331

Explanation:

The Andre's number can consist from 1+1+5 or 3+3+1. There are no any other sets of 3 odd digit to get 7.

Lets prove this statement.

Lets 1 of the digit is bigger than 5. However the digit is odd so it can be 7 only. However in this case the residual 2 digits are 0 . This is not possible so the gigits are odd however 0 is even.

Lets check the case when the biggest digit in the set is smaller than 3.

So it can be 1 only.

So the residual 2 digits can be 1 only. The sum of 1+1+1<7 .

SO we've prooven that the only sets of the digits are 1;1;5 or 3;3;1

The set 1;1;5 can give 3 numbers:

115,151,115

The set 1;3;3 can give 3 numbers as well:

133,313,331