Question

The diagram below shows a pattern made up of toothpicks in the shape of triangles, for the cases of n = 2 and n = 4, where n is the number of toothpicks along the bottom of the pattern.

How many toothpicks are needed for the case of n = 6?
How many toothpicks would be needed for the case of n = 50?

WHAT might be an incorrect solution given by a student? What difficulty or misunderstanding do you think the student is experiencing? Record and Explain the solution/s.

Answer 1

23, 199.

Explanation:

The total number of toothpicks need for n = 6 will be 6 on the bottom line, 6*2 = 12 for forming the triangles, and 6-1 = 5 toothpicks for the top line. That means 5+12+6 = 23.

In general for the case of n toothpicks on the bottom line, we will have (n * 3 ) for the n triangles , and (n-1) toothpicks for the top line for joining the top vertices.

Total = 3n + n-1 = 4n-1 .

For n = 50, the number of toothpicks total = 4*50 - 1 = 199.