SOLUTION: How many integers between 10 and 100 have exactly one digit equal to 3?

Question 13233: How many integers between 10 and 100 have exactly one digit equal to 3?
Found 2 solutions by smik, rapaljer:
Answer by smik(40) (Show Source): You can put this solution on YOUR website!
Well, I'm not sure how you could possibly solve this algebraically, but you can just count the number of integers that have exactly one digit equal to 3.

13, 23, 30, 43, 53, 63, 73, 83, 93 = 9 numbers.
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
Ooops!! In the posted solution for this, smik seems to have missed a few of the possibilities.

These were listed:13, 23, 30, 43, 53, 63, 73, 83, 93 .

Also, the numbers 31, 32, 34, 35, 36, 37, 38, and 39 should have been listed. There is a formula of sorts, there are 9 possibilities for the units digit, and 9 possibilities for the tens digit to be a 3, and then subtract one for the case in which both digits are 3, since that case was counted twice. So there should be 9+9-1 = 17 possibilities. Right?

R^2 at SCC
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