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

(Created page with "== Problem == (a) The <math>3 \times 3</math> square grid has <math>9</math> dots equally spaced. How many squares (of all sizes) can you make using four of these dots as vertic...")
 
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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),dash);
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draw((3,-1)--(3,3),dashed);
  
 
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</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?
 
 
 
  
 
== Solution ==
 
== Solution ==

Revision as of 15:22, 19 October 2014

Problem

(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?

Solution

See also

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