2020 Individual #21
Source:
May 1, 2022
2020 Individual
Problem Statement
Consider the following arrangement of pegs on a board. Jane places three rubber bands on the
pegs on the board such that the following conditions are satisfied:
(I) No two rubber bands cross each other.
(II) Each peg has a rubber band wrapped around it
How many distinct arrangements could Jane create exist? One acceptable arrangement is shown below.
[asy]
size(100);
filldraw(circle((0,0),0.2),black);
filldraw(circle((1,0),0.2),black);
filldraw(circle((2,0),0.2),black);
filldraw(circle((0,1),0.2),black);
filldraw(circle((1,1),0.2),black);
filldraw(circle((2,1),0.2),black);
draw((0,1.2)--(1,1.2));
draw((0,0.8)--(1,0.8));
draw((1,0.2)--(2,0.2));
draw((1,-0.2)--(2,-0.2));
draw((0,0.2)--(2,1.2));
draw((0,-0.2)--(2,0.8));
[/asy]