Hints:

Think about what happens when you add odd numbers together:

• The sum of two odd numbers is even.

• The sum of four, six, or any even number of odd numbers is also even.

So, if you’re adding ten odd numbers, the result must be even — which means a total like 43 is impossible.

The smallest possible sum is when all ten numbers are 1:
→ 1 + 1 + … + 1 = 10

The largest possible sum is when all ten numbers are 9:
→ 9 + 9 + … + 9 = 90

You can increase the total by 2 at a time by replacing a number with the next larger odd number:
→ 10, 12, 14, …, up to 90

Solution:

This puzzle has no solution, and here’s why:

All the numbers you can choose from are odd, and you need to pick ten of them. But when you add an even number of odd numbers, the result is always even.

So no matter which odd numbers you choose, their sum will always be even.

That means a total like 43, which is odd, is impossible to get!