Difference between revisions of "2001 AMC 10 Problems/Problem 5"
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== Problem == | == Problem == | ||
− | How many of the twelve pentominoes pictured below at least one line of symmetry? | + | How many of the twelve pentominoes pictured below have at least one line of reflectional symmetry? |
− | <math> \textbf{(A)} | + | <asy> |
+ | unitsize(5mm); | ||
+ | defaultpen(linewidth(1pt)); | ||
+ | draw(shift(2,0)*unitsquare); | ||
+ | draw(shift(2,1)*unitsquare); | ||
+ | draw(shift(2,2)*unitsquare); | ||
+ | draw(shift(1,2)*unitsquare); | ||
+ | draw(shift(0,2)*unitsquare); | ||
+ | draw(shift(2,4)*unitsquare); | ||
+ | draw(shift(2,5)*unitsquare); | ||
+ | draw(shift(2,6)*unitsquare); | ||
+ | draw(shift(1,5)*unitsquare); | ||
+ | draw(shift(0,5)*unitsquare); | ||
+ | draw(shift(4,8)*unitsquare); | ||
+ | draw(shift(3,8)*unitsquare); | ||
+ | draw(shift(2,8)*unitsquare); | ||
+ | draw(shift(1,8)*unitsquare); | ||
+ | draw(shift(0,8)*unitsquare); | ||
+ | draw(shift(6,8)*unitsquare); | ||
+ | draw(shift(7,8)*unitsquare); | ||
+ | draw(shift(8,8)*unitsquare); | ||
+ | draw(shift(9,8)*unitsquare); | ||
+ | draw(shift(9,9)*unitsquare); | ||
+ | draw(shift(6,5)*unitsquare); | ||
+ | draw(shift(7,5)*unitsquare); | ||
+ | draw(shift(8,5)*unitsquare); | ||
+ | draw(shift(7,6)*unitsquare); | ||
+ | draw(shift(7,4)*unitsquare); | ||
+ | draw(shift(6,1)*unitsquare); | ||
+ | draw(shift(7,1)*unitsquare); | ||
+ | draw(shift(8,1)*unitsquare); | ||
+ | draw(shift(6,0)*unitsquare); | ||
+ | draw(shift(7,2)*unitsquare); | ||
+ | draw(shift(11,8)*unitsquare); | ||
+ | draw(shift(12,8)*unitsquare); | ||
+ | draw(shift(13,8)*unitsquare); | ||
+ | draw(shift(14,8)*unitsquare); | ||
+ | draw(shift(13,9)*unitsquare); | ||
+ | draw(shift(11,5)*unitsquare); | ||
+ | draw(shift(12,5)*unitsquare); | ||
+ | draw(shift(13,5)*unitsquare); | ||
+ | draw(shift(11,6)*unitsquare); | ||
+ | draw(shift(13,4)*unitsquare); | ||
+ | draw(shift(11,1)*unitsquare); | ||
+ | draw(shift(12,1)*unitsquare); | ||
+ | draw(shift(13,1)*unitsquare); | ||
+ | draw(shift(13,2)*unitsquare); | ||
+ | draw(shift(14,2)*unitsquare); | ||
+ | draw(shift(16,8)*unitsquare); | ||
+ | draw(shift(17,8)*unitsquare); | ||
+ | draw(shift(18,8)*unitsquare); | ||
+ | draw(shift(17,9)*unitsquare); | ||
+ | draw(shift(18,9)*unitsquare); | ||
+ | draw(shift(16,5)*unitsquare); | ||
+ | draw(shift(17,6)*unitsquare); | ||
+ | draw(shift(18,5)*unitsquare); | ||
+ | draw(shift(16,6)*unitsquare); | ||
+ | draw(shift(18,6)*unitsquare); | ||
+ | draw(shift(16,0)*unitsquare); | ||
+ | draw(shift(17,0)*unitsquare); | ||
+ | draw(shift(17,1)*unitsquare); | ||
+ | draw(shift(18,1)*unitsquare); | ||
+ | draw(shift(18,2)*unitsquare);</asy> | ||
+ | |||
+ | <math>\textbf{(A) } 3 \qquad\textbf{(B) } 4 \qquad\textbf{(C) } 5 \qquad\textbf{(D) } 6 \qquad\textbf{(E) } 7</math> | ||
== Solution == | == Solution == | ||
− | + | [[File:Pentonimoes.gif]] | |
The ones with lines over the shapes have at least one line of symmetry. Counting the number of shapes that have line(s) on them, | The ones with lines over the shapes have at least one line of symmetry. Counting the number of shapes that have line(s) on them, | ||
Line 15: | Line 79: | ||
{{AMC10 box|year=2001|num-b=4|num-a=6}} | {{AMC10 box|year=2001|num-b=4|num-a=6}} | ||
+ | {{MAA Notice}} |
Latest revision as of 13:51, 7 August 2023
Problem
How many of the twelve pentominoes pictured below have at least one line of reflectional symmetry?
Solution
The ones with lines over the shapes have at least one line of symmetry. Counting the number of shapes that have line(s) on them, we find pentominoes.
See Also
2001 AMC 10 (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.