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# counting

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How many 3-digit numbers have the property that the units digit is at least twice the tens digit plus 5?

Jun 26, 2022

#1
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There are 9 choices for the hundreds digit.

The only possible cases for the tens and units digits are: (0, 5 - 9), (1, 7 - 9), (2, 9)

This makes for 9 cases for the units and tens digits.

Thus, there are $$9 \times 9 = \color{brown}\boxed{81}$$ cases.

Jun 26, 2022