2013 AMC 8 Problem 22

Below is the video solution and professionally curated solution for Problem 22 of the 2013 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2013 AMC 8 solutions, or check the answer key.

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Concepts:basic counting

Difficulty rating: 1280

22.

Toothpicks are used to make a grid that is 6060 toothpicks long and 3232 toothpicks high. How many toothpicks are used altogether?

19201920

19521952

19801980

20132013

39323932

Video solution:
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Written solution:

A 6060-by-3232 grid has 6161 vertical grid lines, each made of 3232 toothpicks, and 3333 horizontal grid lines, each made of 6060 toothpicks.

Therefore the total number of toothpicks is 6132+3360=1952+1980=3932.61\cdot32+33\cdot60=1952+1980=3932.

Thus, E is the correct answer.

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