2017 AMC 10 B

Complete problem set with solutions and individual problem pages

Problem 16 Medium

How many of the base-ten numerals for the positive integers less than or equal to 2017 contain the digit 0? (2017 AMC 10B Problem, Question#16)

  • A.

    469

  • B.

    471

  • C.

    475

  • D.

    478

  • E.

    481

Answer:A

We can use complementary counting. There are 2017 positive integers in total to consider, and there are 9 one-digit integers, 9\cdot 9=81 two digit integers without a zero, 9\cdot 9\cdot 9 three digit integers without a zero, and 9\cdot 9\cdot 9=729 four-digit integers starting with a 1without a zero. Therefore, the answer is 2017-9-81-729-729=469.