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

## 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?