Difference between revisions of "2010 UNCO Math Contest II Problems/Problem 11"
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draw((0,0)--(1,0)--(1,1)--(0,1)--cycle,black); | draw((0,0)--(1,0)--(1,1)--(0,1)--cycle,black); | ||
draw((4,1)--(5,0)--(6,1)--(5,2)--cycle,black); | draw((4,1)--(5,0)--(6,1)--(5,2)--cycle,black); | ||
| − | draw((3,-1)--(3,3), | + | draw((3,-1)--(3,3),dashed); |
</asy> | </asy> | ||
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(d) How many for an <math>(N+1) \times (N+1)</math> grid of dots? | (d) How many for an <math>(N+1) \times (N+1)</math> grid of dots? | ||
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== Solution == | == Solution == | ||
Revision as of 16:22, 19 October 2014
Problem
(a) The 
square grid has 
dots equally
spaced. How many squares (of all sizes)
can you make using four of these dots
as vertices? Two examples are shown.
![[asy] for (int x=0; x<3; ++x) {for (int y=0; y<3; ++y) {dot((x,y));dot((x+4,y));} } draw((0,0)--(1,0)--(1,1)--(0,1)--cycle,black); draw((4,1)--(5,0)--(6,1)--(5,2)--cycle,black); draw((3,-1)--(3,3),dashed); [/asy]](http://latex.artofproblemsolving.com/2/5/c/25cf0db35690d9453f4c01ff44569a8e74957ba1.png)
(b) How many for a 
?
(c) How many for a 
?
(d) How many for an 
grid of dots?
