2001 AMC 10 Problem 5

How many of the twelve pentominoes pictured below have at least one line of symmetry?

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Solution

Checking each pentomino for a reflection line, exactly six have at least one: the straight bar, the plus, the

T

-shape, the

U

-shape, the

V

-shape, and the

W

-shape. The remaining six have no line of symmetry. Thus, the correct answer is D.

Concepts: symmetry · systematic listing

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.