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How many 3-digit numbers have the units digit larger than the tens digit?

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Take a look in each hundred numbers starting with the digit x:
x10 x20 ... x90 - 9 of them
x21 x31 ... x91 - 8 of them
...
x98 - 1 of them
9+8+...+1 = 45
So, in each hundred numbers there are 45 that have the tens greater than the ones.

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