Problem:
Toothpicks of equal length are used to build a rectangular grid as shown. If the grid is toothpicks high and toothpicks wide, then the number of toothpicks used is
.jpg)
Answer Choices:
A.
B.
C.
D.
E.
Solution:
For an grid there are columns of vertical toothpicks, each toothpicks long. Thus, there are () vertical toothpicks. Likewise, there are horizontal toothpicks. The total is toothpicks. In our case with and , the number of toothpicks is .
Each of the unit squares has four sides. Thus counts each toothpick twice, except for the toothpicks on the perimeter of the rectangle, which are only counted once. Hence, the number of toothpicks is .