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2012 UNCO Math Contest II Problems/Problem 3

Revision as of 02:19, 17 October 2014 by Timneh (talk | contribs) (Created page with "== Problem == Mrs. Olson begins a journey at the intersection of Avenue <math>A</math> and First Street in the upper left on the attached map. She ends her journey at one of th...")
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Problem

Mrs. Olson begins a journey at the intersection of Avenue $A$ and First Street in the upper left on the attached map. She ends her journey at one of the Starbucks on Avenue $D$. There is a Starbucks on Avenue $D$ at every intersection from First Street through Sixth Street! If Mrs. Olson walks only East and South, how many different paths to a Starbucks on Avenue $D$ can she take? Note that Mrs. Olson may pass one Starbucks on her way to another Starbucks farther to the East.

[asy] size(300,100); path R=((0,0)--(0,1)--(2,1)--(2,0)--cycle); for(int rw=0;rw<5;++rw){ for (int cl=0;cl<7;++cl){ filldraw(shift(3*cl,2*rw)*R,green);} } MP("Avenue \: D",(12,1+.5),E); MP("Avenue \: C",(12,3+.5),E); MP("Avenue \: B",(0,5+.5),E); MP("Avenue \: A",(0,7+.5),E); MP(90,"1st\: Street",(3-.5,0),N); MP(90,"2cnd\: Street",(6-.5,0),N); MP(90,"3rd\: Street",(9-.5,0),N); MP(90,"4th\: Street",(12-.5,4),N); MP(90,"5th\: Street",(15-.5,4),N); MP(90,"6th\: Street",(18-.5,4),N); [/asy]


Solution

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