No Fours or Fives

64, or if you don't count, 00, 01, 02, 03, 06, 07, 08, 09, then 56.

How did you figure that? You see, my homework asks not just the answers, but how I arrived at that. Don't give me the answers though. Help me figure out the answers so I can learn.

Thanks, Primo

It's not so much "math", more plain ol' fashioned sitting down and thinking. Using all the digits 0 to 9, and ignoring 00 to 09, you can make 9 decades, that is 90 two digit numbers, from 10 to 99. You can take out the 40 and 50 decades straight away. That leaves 7 decades, 70 numbers. Take out 2 (the -4 and -5 numbers) from each decade. There are 14 of these. Now you have 56 numbers left.

Think of it as a permutation problem. You are going to select two numbers. The first number has how many possibilities? (You can't use 0, 4 or 5). The second number has how many? (You can't use 4 or 5). The product of those two numbers is the answer.

well done, Engineer.