Problem #2337

2337.

Ann made a 3-step staircase using 18 toothpicks as shown in the figure. How many toothpicks does she need to add to complete a 5-step staircase?

[asy] unitsize(40); for(int i=0; i<3; i+=1) { draw((0,i+0.05)--(0,i+0.95)); draw((i+0.05,0)--(i+0.95,0)); for(int j=0; j<3-i; j+=1) { draw((i+1,j+0.05)--(i+1,j+0.95)); draw((i+0.05,j+1)--(i+0.95,j+1)); } } [/asy]

$\textbf{(A)}\ 9\qquad\textbf{(B)}\ 18\qquad\textbf{(C)}\ 20\qquad\textbf{(D)}\ 22\qquad\textbf{(E)}\ 24$

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Instructions for entering answers:

  • Reduce fractions to lowest terms and enter in the form 7/9.
  • Numbers involving pi should be written as 7pi or 7pi/3 as appropriate.
  • Square roots should be written as sqrt(3), 5sqrt(5), sqrt(3)/2, or 7sqrt(2)/3 as appropriate.
  • Exponents should be entered in the form 10^10.
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