Difference between revisions of "1993 AJHSME Problems/Problem 13"
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==Problem== | ==Problem== | ||
| − | The word "'''HELP'''" in block letters is painted in black with strokes <math>1</math> unit wide on a <math>5</math> by <math>15</math> rectangular white sign with dimensions as shown. The area of the white portion of the sign, in square units, is | + | The word "'''HELP'''" in block letters is painted in black with strokes <math>1</math> unit wide on a <math>5</math> by <math>15</math> rectangular white sign with dimensions as shown. The area of the white portion of the sign, in square units, is? |
<asy> | <asy> | ||
| Line 11: | Line 11: | ||
fill((13,3)--(14,3)--(14,4)--(13,4)--cycle,white); | fill((13,3)--(14,3)--(14,4)--(13,4)--cycle,white); | ||
draw((0,0)--(15,0)--(15,5)--(0,5)--cycle); | draw((0,0)--(15,0)--(15,5)--(0,5)--cycle); | ||
| − | label("$5\left\{ \begin{tabular}{c} | + | label("$5\left\{ \begin{tabular}{c} <br /> <br /> <br /> <br /> \end{tabular}\right.$",(1,2.5),W); |
label(rotate(90)*"$\{$",(0.5,0.1),S); | label(rotate(90)*"$\{$",(0.5,0.1),S); | ||
label("$1$",(0.5,-0.6),S); | label("$1$",(0.5,-0.6),S); | ||
| Line 20: | Line 20: | ||
label(rotate(90)*"$\{$",(11.5,0.1),S); | label(rotate(90)*"$\{$",(11.5,0.1),S); | ||
label("$1$",(11.5,-0.6),S); | label("$1$",(11.5,-0.6),S); | ||
| − | label(rotate(270)*"$\left\{ \begin{tabular}{c} | + | label(rotate(270)*"$\left\{ \begin{tabular}{c} <br /> <br /> \end{tabular}\right.$",(1.5,4),N); |
label("$3$",(1.5,5.8),N); | label("$3$",(1.5,5.8),N); | ||
| − | label(rotate(270)*"$\left\{ \begin{tabular}{c} | + | label(rotate(270)*"$\left\{ \begin{tabular}{c} <br /> <br /> \end{tabular}\right.$",(5.5,4),N); |
label("$3$",(5.5,5.8),N); | label("$3$",(5.5,5.8),N); | ||
| − | label(rotate(270)*"$\left\{ \begin{tabular}{c} | + | label(rotate(270)*"$\left\{ \begin{tabular}{c} <br /> <br /> \end{tabular}\right.$",(9.5,4),N); |
label("$3$",(9.5,5.8),N); | label("$3$",(9.5,5.8),N); | ||
| − | label(rotate(270)*"$\left\{ \begin{tabular}{c} | + | label(rotate(270)*"$\left\{ \begin{tabular}{c} <br /> <br /> \end{tabular}\right.$",(13.5,4),N); |
label("$3$",(13.5,5.8),N); | label("$3$",(13.5,5.8),N); | ||
| − | label("$\left. \begin{tabular}{c} | + | label("$\left. \begin{tabular}{c} <br /> \end{tabular}\right\} 2$",(14,1),E); |
</asy> | </asy> | ||
Revision as of 22:41, 24 October 2018
Problem
The word "HELP" in block letters is painted in black with strokes 
unit wide on a 
by 
rectangular white sign with dimensions as shown. The area of the white portion of the sign, in square units, is?
![[asy] unitsize(12); fill((0,0)--(0,5)--(1,5)--(1,3)--(2,3)--(2,5)--(3,5)--(3,0)--(2,0)--(2,2)--(1,2)--(1,0)--cycle,black); fill((4,0)--(4,5)--(7,5)--(7,4)--(5,4)--(5,3)--(7,3)--(7,2)--(5,2)--(5,1)--(7,1)--(7,0)--cycle,black); fill((8,0)--(8,5)--(9,5)--(9,1)--(11,1)--(11,0)--cycle,black); fill((12,0)--(12,5)--(15,5)--(15,2)--(13,2)--(13,0)--cycle,black); fill((13,3)--(14,3)--(14,4)--(13,4)--cycle,white); draw((0,0)--(15,0)--(15,5)--(0,5)--cycle); label("$5\left\{ \begin{tabular}{c} <br /> <br /> <br /> <br /> \end{tabular}\right.$",(1,2.5),W); label(rotate(90)*"$\{$",(0.5,0.1),S); label("$1$",(0.5,-0.6),S); label(rotate(90)*"$\{$",(3.5,0.1),S); label("$1$",(3.5,-0.6),S); label(rotate(90)*"$\{$",(7.5,0.1),S); label("$1$",(7.5,-0.6),S); label(rotate(90)*"$\{$",(11.5,0.1),S); label("$1$",(11.5,-0.6),S); label(rotate(270)*"$\left\{ \begin{tabular}{c} <br /> <br /> \end{tabular}\right.$",(1.5,4),N); label("$3$",(1.5,5.8),N); label(rotate(270)*"$\left\{ \begin{tabular}{c} <br /> <br /> \end{tabular}\right.$",(5.5,4),N); label("$3$",(5.5,5.8),N); label(rotate(270)*"$\left\{ \begin{tabular}{c} <br /> <br /> \end{tabular}\right.$",(9.5,4),N); label("$3$",(9.5,5.8),N); label(rotate(270)*"$\left\{ \begin{tabular}{c} <br /> <br /> \end{tabular}\right.$",(13.5,4),N); label("$3$",(13.5,5.8),N); label("$\left. \begin{tabular}{c} <br /> \end{tabular}\right\} 2$",(14,1),E); [/asy]](http://latex.artofproblemsolving.com/e/6/0/e60c9a023f0dd6394146e0efe9475a00667e7993.png)
Solution
Count the number of black squares in each letter. H has 11, E has 11, L has 7, and P has 10, giving the number of black squares to be 
. The total number of squares is 
and the number of white squares is 
.
See Also
| 1993 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 12 |
Followed by Problem 14 | |
| 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. 
