2017 AMC 10 B

Complete problem set with solutions and individual problem pages

Problem 18 Medium

In the figure below, 3 of the 6 disks are to be painted blue, 2 are to be painted red, and 1 is to be painted green. Two paintings that can be obtained from one another by a rotation or a reflection of the entire figure are considered the same. How many different paintings are possible? (2017 AMC 10B Problem, Question#18)

  • A.

    6

  • B.

    8

  • C.

    9

  • D.

    12

  • E.

    15

Answer:D

First we figure out the number of ways to put the blue 3 disks. Denote the spots to put the disks as 1-6 from left to right, top to bottom. The cases to put the blue disks are (1,2,3,(1,2,4),(1,2,5),(1,2,6),(2,3,5),(1,4,6). For each of those cases we can easily figure out the number of ways for each case, so the total amount is 2+2+3+3+1+1=12.

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