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2004 AMC 10B Problem 2

Problem 2 of 25EasierNumber TheoryCombinatorics

How many two-digit positive integers have at least one 77 as a digit?

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Solution

The numbers 7070 through 7979 give 1010 with a 77 in the tens place. The numbers 17,27,…,9717, 27, \ldots, 97 give 99 with a 77 in the units place. Since 7777 is counted twice, the total is 10+9−1=18.10 + 9 - 1 = 18. Thus, the correct answer is B.
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Tagged: digits · inclusion-exclusion

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