2017 AMC 10 B

Complete problem set with solutions and individual problem pages

Problem 6 Easy

What is the largest number of solid 2-in \times 2-in \times 1-in blocks that can fit in a 3-in \times 2-in \times 3-in box? (2017 AMC 10B Problem, Question#6)

  • A.

    3

  • B.

    4

  • C.

    5

  • D.

    6

  • E.

    7

Answer:B

We find that the volume of the larger block is 18, and the volume of the smaller block is 4. Dividing the two, we see that only a maximum of four 2 by 2 by 1 blocks can fit inside the 3 by 3 by 2 block. Drawing it out, we see that such a configuration is indeed possible. Therefore, the answer is 4.

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