Difference between revisions of "2013 UNCO Math Contest II Problems/Problem 11"
(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...") |
m (moved 2013 UNC Math Contest II Problems/Problem 11 to 2013 UNCO Math Contest II Problems/Problem 11: disambiguation of University of Northern Colorado with University of North Carolina) |
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Revision as of 17:23, 19 October 2014
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)
