# 1993 AJHSME Problems/Problem 13

## Problem

The word "HELP" in block letters is painted in black with strokes $1$ unit wide on a $5$ by $15$ rectangular white sign with dimensions as shown. The area of the white portion of the sign, in square units, is $[asy] unitsize(12); fill((0,0)--(0,5)--(1,5)--(1,3)--(2,3)--(2,5)--(3,5)--(3,0)--(2,0)--(2,2)--(1,2)--(1,0)--cycle,black); fill((4,0)--(4,5)--(7,5)--(7,4)--(5,4)--(5,3)--(7,3)--(7,2)--(5,2)--(5,1)--(7,1)--(7,0)--cycle,black); fill((8,0)--(8,5)--(9,5)--(9,1)--(11,1)--(11,0)--cycle,black); fill((12,0)--(12,5)--(15,5)--(15,2)--(13,2)--(13,0)--cycle,black); fill((13,3)--(14,3)--(14,4)--(13,4)--cycle,white); draw((0,0)--(15,0)--(15,5)--(0,5)--cycle); label("5\left\{ \begin{tabular}{c} \\ \\ \\ \\ \end{tabular}\right.",(1,2.5),W); label(rotate(90)*"\{",(0.5,0.1),S); label("1",(0.5,-0.6),S); label(rotate(90)*"\{",(3.5,0.1),S); label("1",(3.5,-0.6),S); label(rotate(90)*"\{",(7.5,0.1),S); label("1",(7.5,-0.6),S); label(rotate(90)*"\{",(11.5,0.1),S); label("1",(11.5,-0.6),S); label(rotate(270)*"\left\{ \begin{tabular}{c} \\ \\ \end{tabular}\right.",(1.5,4),N); label("3",(1.5,5.8),N); label(rotate(270)*"\left\{ \begin{tabular}{c} \\ \\ \end{tabular}\right.",(5.5,4),N); label("3",(5.5,5.8),N); label(rotate(270)*"\left\{ \begin{tabular}{c} \\ \\ \end{tabular}\right.",(9.5,4),N); label("3",(9.5,5.8),N); label(rotate(270)*"\left\{ \begin{tabular}{c} \\ \\ \end{tabular}\right.",(13.5,4),N); label("3",(13.5,5.8),N); label("\left. \begin{tabular}{c} \\ \end{tabular}\right\} 2",(14,1),E); [/asy]$ $\text{(A)}\ 30 \qquad \text{(B)}\ 32 \qquad \text{(C)}\ 34 \qquad \text{(D)}\ 36 \qquad \text{(E)}\ 38$

## 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 $11+11+7+10=39$. The total number of squares is $(15)(5)=75$ and the number of white squares is $75-39=\boxed{\text{(D)}\ 36}$.

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 