How many ways can you get the smallest sum adding two-digit numbers if none of the digits can repeat?

Question

3rd grade homework

Answer 1

Let’s take the smallest digits: 0, 1, 2, 3.

The zero must be the ones digit to create a 2-digit number. So we can have 10 as one of the numbers. The smallest number we can get from 2 and 3 is 23.

Therefore we have 10+23=33 A’s one sum. But we can also have 20+13=33.

We can also write 23+10=33 and 13+20=33, which are really the same thing if the order of the numbers doesn’t count. So there seem to be two ways, if the order doesn’t matter.