imc

Question

Sara makes a staircase out of toothpicks as shown: FIGURE This is a 3-step staircase and uses 18 toothpicks. How many steps would be in a staircase that used 180 toothpicks?

Accepted Answer

A staircase with n steps contains 4 + 6 + 8 + ... + 2n + 2 toothpicks. This can be rewritten as (n+1)(n+2) -2. So, (n+1)(n+2) - 2 = 180 So, (n+1)(n+2) = 182. Inspection could tell us that 13 14 = 182, so the answer is 13 - 1 = 12