2020 AMC 8 Problems/Problem 21
Revision as of 00:37, 18 November 2020 by Icematrix2 (talk | contribs)
Problem 21
A game board consists of 
squares that alternate in color between black and white. The figure below shows square 
in the bottom row and square 
in the top row. A marker is placed at 
A step consists of moving the marker onto one of the adjoining white squares in the row above. How many 
-step paths are there from to 
(The figure shows a sample path.)
![[asy] size(200); int[] x = {6, 5, 4, 5, 6, 5, 6}; int[] y = {1, 2, 3, 4, 5, 6, 7}; int N = 7; for (int i = 0; i < 8; ++i) { for (int j = 0; j < 8; ++j) { draw((i,j)--(i+1,j)--(i+1,j+1)--(i,j+1)--(i,j)); if ((i+j) % 2 == 0) { filldraw((i,j)--(i+1,j)--(i+1,j+1)--(i,j+1)--(i,j)--cycle,black); } } } for (int i = 0; i < N; ++i) { draw(circle((x[i],y[i])+(0.5,0.5),0.35)); } label("$P$", (5.5, 0.5)); label("$Q$", (6.5, 7.5)); [/asy]](http://latex.artofproblemsolving.com/8/4/3/843f961c831f9ff7600db891b2cb6ee8944436fb.png)
![\[\text{Diagram by sircalcsalot}\]](http://latex.artofproblemsolving.com/9/8/b/98bb15c1c3b19c2e76eaf41d62e0accd5506ef29.png)
See also
| 2020 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 20 |
Followed by Problem 22 | |
| 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 AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
