Difference between revisions of "2006 UNCO Math Contest II Problems/Problem 11"
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==Solution== | ==Solution== | ||
| − | {{ | + | <math>\binom{7}{4}</math> in general <math>\binom{n+3}{4}</math> |
==See Also== | ==See Also== | ||
{{UNCO Math Contest box|n=II|year=2006|num-b=10|after=Last Question}} | {{UNCO Math Contest box|n=II|year=2006|num-b=10|after=Last Question}} | ||
[[Category: Intermediate Geometry Problems]] | [[Category: Intermediate Geometry Problems]] | ||
Latest revision as of 02:35, 13 January 2019
Problem
Call the figure below a "
-tableau" shape. Determine the number of rectangles of all sizes contained within this shape.
Note that a square is considered a rectangle, and a 
rectangle is considered different from a 
.
Express your answer as a binomial coefficient and explain the significance of your expression. Generalize, with proof, to an "
-tableau" shape.
![[asy] for(int j=0;j<5;++j){ draw((0,j)--(min(j+1,4),j),black); draw((j,max(0,j-1))--(j,4),black); } filldraw((2,2)--(2,3)--(1,3)--(1,2)--cycle,blue); filldraw((2,2)--(3,2)--(3,3)--(2,3)--cycle,blue); [/asy]](http://latex.artofproblemsolving.com/4/0/7/40701260398d42e58abedffd16b69fb89e5e4c30.png)
Solution
in general 
See Also
| 2006 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 10 |
Followed by Last Question | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
| All UNCO Math Contest Problems and Solutions | ||
