Question

How many positive 3-digit numbers have property that the first digit is at least three times the second digit?

Answer 1

The number of positive 3-digit numbers have a property that the first digit is at least three times the second digit is 285.

How to get the number?

Since restriction is set to the first digit, all you have to think is about the last two digits e.g if the first digit is one, the last two digits can only be zeros.

Thus, by the principle of multiplication, 1×1=1 way. If the first digit is 2, then the last digits can be either 1 or 0. You have 2×2=4 ways

For first digit 3, the last two digits can be 0,1 or 2. 3x3=9, there is a succinct pattern. Therefore, 1+4+9+16+25+36+49+64+81=285.

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