2015 AMC 10A Problems/Problem 3
Contents
[hide]Problem
Ann made a -step staircase using toothpicks as shown in the figure. How many toothpicks does she need to add to complete a -step staircase?
Solution
We can see that a -step staircase requires toothpicks and a -step staircase requires toothpicks. Thus, to go from a -step to -step staircase, additional toothpicks are needed and to go from a -step to -step staircase, additional toothpicks are needed. Applying this pattern, to go from a -step to -step staircase, additional toothpicks are needed and to go from a -step to -step staircase, additional toothpicks are needed. Our answer is
Solution 2
Alternatively, we can see with the -step staircase has toothpicks. Generalizing, we see that a staircase with steps has toothpicks. So, for steps, we have toothpicks. So our answer is or .
See Also
2015 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
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All AMC 10 Problems and Solutions |
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