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
Answer Choices:
A. 30
B. 32
C. 34
D. 36
E. 38
Solution:
The white portion can be partitioned into rectangles as shown.
The sum of the areas of the white rectangles is 4(2)+3(5)+8+1+4=36.
OR
Compute the area of the black letters and subtract it from 5×15=75, the total area of the sign:
H:E:L:P:​2(1×5)+1×1=11,1×5+3(2×1)=11,1×5+1×2=7,1×5+2(1×1)+1×3=10.​
The area of the white portion is 75−(11+11+7+10)=36.
OR
Superimpose a 1×1 grid on the sign and count the 36 white squares:
Answer: D​.
The problems on this page are the property of the MAA's American Mathematics Competitions
