Difference between revisions of "2015 AMC 10A Problems/Problem 3"
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<math>\textbf{(A)}\ 9\qquad\textbf{(B)}\ 18\qquad\textbf{(C)}\ 20\qquad\textbf{(D)}\ 22\qquad\textbf{(E)}\ 24</math> | <math>\textbf{(A)}\ 9\qquad\textbf{(B)}\ 18\qquad\textbf{(C)}\ 20\qquad\textbf{(D)}\ 22\qquad\textbf{(E)}\ 24</math> | ||
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+ | <asy> | ||
+ | size(150); | ||
+ | defaultpen(linewidth(0.8)); | ||
+ | path h = ellipse((0.5,0),0.45,0.015), v = ellipse((0,0.5),0.015,0.45); | ||
+ | for(int i=0;i<=2;i=i+1) | ||
+ | { | ||
+ | for(int j=0;j<=3-i;j=j+1) | ||
+ | { | ||
+ | filldraw(shift((i,j))*h,black); | ||
+ | filldraw(shift((j,i))*v,black); | ||
+ | } | ||
+ | }</asy> | ||
==Solution== | ==Solution== |
Revision as of 18:16, 17 July 2015
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
See Also
2015 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.