Square Pattern
Source:
January 24, 2006
algebrapolynomialfunctionquadraticsgeometryinductionAMC
Problem Statement
Figures , , , and consist of , , , and nonoverlapping squares, respectively. If the pattern were continued, how many nonoverlapping squares would there be in figure ?
[asy]
unitsize(8);
draw((0,0)--(1,0)--(1,1)--(0,1)--cycle);
draw((9,0)--(10,0)--(10,3)--(9,3)--cycle);
draw((8,1)--(11,1)--(11,2)--(8,2)--cycle);
draw((19,0)--(20,0)--(20,5)--(19,5)--cycle);
draw((18,1)--(21,1)--(21,4)--(18,4)--cycle);
draw((17,2)--(22,2)--(22,3)--(17,3)--cycle);
draw((32,0)--(33,0)--(33,7)--(32,7)--cycle);
draw((29,3)--(36,3)--(36,4)--(29,4)--cycle);
draw((31,1)--(34,1)--(34,6)--(31,6)--cycle);
draw((30,2)--(35,2)--(35,5)--(30,5)--cycle);
label("Figure",(0.5,-1),S);
label("",(0.5,-2.5),S);
label("Figure",(9.5,-1),S);
label("",(9.5,-2.5),S);
label("Figure",(19.5,-1),S);
label("",(19.5,-2.5),S);
label("Figure",(32.5,-1),S);
label("",(32.5,-2.5),S);[/asy]