Difference between revisions of "2010 UNCO Math Contest II Problems/Problem 11"

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== See also ==
== See also ==
{{UNC Math Contest box|year=2010|n=II|num-b=10|after=Last Question}}
{{UNCO Math Contest box|year=2010|n=II|num-b=10|after=Last Question}}
[[Category:Intermediate Combinatorics Problems]]
[[Category:Intermediate Combinatorics Problems]]

Revision as of 20:32, 19 October 2014


(a) The $3 \times 3$ square grid has $9$ 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]

(b) How many for a $4 \times 4$?

(c) How many for a $5 \times 5$?

(d) How many for an $(N+1) \times (N+1)$ grid of dots?


See also

2010 UNCO Math Contest II (ProblemsAnswer KeyResources)
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