imc

Question

A large equilateral triangle is constructed by using toothpicks to create rows of small equilateral triangles. For example, in the figure, we have 3 rows of small congruent equilateral triangles, with 5 small triangles in the base row. How many toothpicks would be needed to construct a large equilateral triangle if the base row of the triangle consists of 2003 small equilateral triangles? FIGURE

Accepted Answer

There are 1+3+5+...+2003=1002^2=1004004 small equilateral triangles. Each small equilateral triangle needs 3 toothpicks to make it. But, each toothpick that isn't one of the 10023=3006 toothpicks on the outside of the large equilateral triangle is a side for 2 small equilateral triangles. So, the number of toothpicks on the inside of the large equilateral triangle is 100400043-30062=1504503 Therefore the total number of toothpicks is 1504503+3006=1,507,509