Difference between revisions of "2005 AMC 8 Problems/Problem 3"
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− | ==Problem== | + | == Problem == |
What is the minimum number of small squares that must be colored black so that a line of symmetry lies on the diagonal <math> \overline{BD}</math> of square <math> ABCD</math>? | What is the minimum number of small squares that must be colored black so that a line of symmetry lies on the diagonal <math> \overline{BD}</math> of square <math> ABCD</math>? | ||
− | <asy>defaultpen(linewidth(1)); | + | |
+ | <asy> | ||
+ | defaultpen(linewidth(1)); | ||
for ( int x = 0; x < 5; ++x ) | for ( int x = 0; x < 5; ++x ) | ||
{ | { | ||
Line 15: | Line 17: | ||
label("$B$", (4, 4), NE); | label("$B$", (4, 4), NE); | ||
label("$C$", (4, 0), SE); | label("$C$", (4, 0), SE); | ||
− | label("$D$", (0, 0), SW);</asy> | + | label("$D$", (0, 0), SW); |
+ | </asy> | ||
<math> \textbf{(A)}\ 1\qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ 3\qquad\textbf{(D)}\ 4\qquad\textbf{(E)}\ 5 </math> | <math> \textbf{(A)}\ 1\qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ 3\qquad\textbf{(D)}\ 4\qquad\textbf{(E)}\ 5 </math> | ||
− | ==Solution== | + | == Solution == |
Rotating square <math>ABCD</math> counterclockwise <math>45^\circ</math> so that the line of symmetry <math>BD</math> is a vertical line makes it easier to see that <math>\boxed{\textbf{(D)}\ 4}</math> squares need to be colored to match its corresponding square. | Rotating square <math>ABCD</math> counterclockwise <math>45^\circ</math> so that the line of symmetry <math>BD</math> is a vertical line makes it easier to see that <math>\boxed{\textbf{(D)}\ 4}</math> squares need to be colored to match its corresponding square. | ||
− | ==See Also== | + | == See Also == |
{{AMC8 box|year=2005|num-b=2|num-a=4}} | {{AMC8 box|year=2005|num-b=2|num-a=4}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Latest revision as of 12:33, 19 October 2020
Problem
What is the minimum number of small squares that must be colored black so that a line of symmetry lies on the diagonal of square ?
Solution
Rotating square counterclockwise so that the line of symmetry is a vertical line makes it easier to see that squares need to be colored to match its corresponding square.
See Also
2005 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
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 AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.