2013 UNCO Math Contest II Problems/Problem 11: Difference between revisions
Created page with "== Problem == (a) Stages <math>1</math> and <math>2</math> each contain <math>1</math> tile. Stage <math>6</math> contains <math>8</math> tiles. If the pattern is continued, ho..." |
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== Solution == | == Solution == | ||
(a) <math>610</math> (b) <math>60^{th}</math> | |||
== See Also == | == See Also == | ||
{{ | {{UNCO Math Contest box|n=II|year=2013|num-b=10|after=Last Question}} | ||
[[Category:Intermediate Algebra Problems]] | [[Category:Intermediate Algebra Problems]] | ||
Latest revision as of 02:30, 13 January 2019
Problem
(a) Stages 
and 
each contain tile. Stage 
contains 
tiles. If
the pattern is continued, how many tiles will Stage 
contain?
(b) What is the first Stage in which the number of tiles is a multiple
of 
?
![[asy] size(14cm,0); draw((0,0)--(1,1)--(2,1)--cycle,black); draw((3,0)--(4,2)--(5,0)--cycle,black); draw((6,0)--(7,2)--(8,0)--cycle,black); draw((6,0)--(5.5,-1)--(8,0)--cycle,black); draw((9,0)--(10,2)--(11,0)--cycle,black); draw((9,0)--(8.5,-1)--(11,0)--cycle,black); draw((8.5,-1)--(11,0)--(11.5,-1)--cycle,black); draw((13,0)--(14,2)--(15,0)--cycle,black); draw((13,0)--(12.5,-1)--(15,0)--cycle,black); draw((12.5,-1)--(15,0)--(15.5,-1)--cycle,black); draw((12.5,-1)--(11.5,-3)--(15.5,-1)--cycle,black); draw((12.5,-1)--(14,-1.75),black); draw((18,0)--(19,2)--(20,0)--cycle,black); draw((18,0)--(17.5,-1)--(20,0)--cycle,black); draw((17.5,-1)--(20,0)--(20.5,-1)--cycle,black); draw((17.5,-1)--(16.5,-3)--(20.5,-1)--cycle,black); draw((17.5,-1)--(21.5,-3)--(20.5,-1)--cycle,black); draw((16.5,-3)--(21.5,-3),black); draw((19,-1.75)--(20,-3),black); MP("Stage 1",(.5,-3)); MP("Stage 2",(3.5,-3)); MP("Stage 3",(6.5,-3)); MP("Stage 4",(10,-3)); MP("Stage 5",(14,-3)); MP("Stage 6",(19,-3)); [/asy]](http://latex.artofproblemsolving.com/7/d/7/7d7455610c97f6bf1748c0261325fb15d38051ca.png)
Solution
(a) 
(b) 
See Also
| 2013 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 | ||
