Q:

How many two digit whole numbers can be written as the sum of two different single digit whole numbers? Lots of points, and will give brainliest! Please help!

Accepted Solution

A:
You want [tex] x+y>9 [/tex]. We can go about this by casework. WLOG x=9, we have 8 digits: 1-8. With x=8 we have 2-9, but we already counted 8 and we already considered the 9 case, so we have 2-7 actually, which will give us 6 numbers. With x=7, with the same logic we are only looking for the numbers 3-6 which there are 4 of. With x=6, you are looking for the numbers 4-5 which are 2. With x=5 run out of numbers to pick. The numbers are indistinguishable and it does not matter whether we use x or y so we just have to ad up the cases we already have to get: 20.