Turkey Junior Olympiad 2002, Part II - P2
Source:
January 18, 2013
induction
Problem Statement
[asy]
unitsize(11);
for(int i=0; i<6; ++i)
{
if(i<5)
draw( (i, 0)--(i,5) );
else draw( (i, 0)--(i,2) ); if(i < 3)
draw((0,i)--(5,i));
else draw((0,i)--(4,i));
}
[/asy]
We are dividing the above figure into parts with shapes: [asy]unitsize(11);
draw((0,0)--(0,2));
draw((1,0)--(1,2));
draw((2,1)--(2,2));
draw((0,0)--(1,0));
draw((0,1)--(2,1));
draw((0,2)--(2,2));
[/asy][asy]
unitsize(11);
draw((0,0)--(0,2));
draw((1,0)--(1,2));
draw((2,1)--(2,2));
draw((3,1)--(3,2));
draw((0,0)--(1,0));
draw((0,1)--(3,1));
draw((0,2)--(3,2));
[/asy]
After that division, find the number of
[asy]unitsize(11);
draw((0,0)--(0,2));
draw((1,0)--(1,2));
draw((2,1)--(2,2));
draw((0,0)--(1,0));
draw((0,1)--(2,1));
draw((0,2)--(2,2));
[/asy]
shaped parts.