2013 UNCO Math Contest II Problems/Problem 11
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)
