Difference between revisions of "2010 UNCO Math Contest II Problems/Problem 11"
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== Solution == | == Solution == | ||
| + | (a) <math>6</math> (b) <math>20</math> (c) <math>50</math> (d) <math>1\cdot n^2 + 2\cdot (n-1)^2+3\cdot (n-2)^2 + \cdots + n\cdot 1^2</math> | ||
== See also == | == See also == | ||
| − | {{ | + | {{UNCO Math Contest box|year=2010|n=II|num-b=10|after=Last Question}} |
[[Category:Intermediate Combinatorics Problems]] | [[Category:Intermediate Combinatorics Problems]] | ||
Latest revision as of 00:58, 2 February 2023
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?
Solution
(a) 
(b) 
(c) 
(d) 
See also
| 2010 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 | ||
