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

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.