Plus Minus Pyramids
Source: 2018 AMC 8 #19
November 20, 2018
geometry3D geometrypyramidAMC 82018 AMC 8
Problem Statement
In a sign pyramid a cell gets a "+" if the two cells below it have the same sign, and it gets a "-" if the two cells below it have different signs. The diagram below illustrates a sign pyramid with four levels. How many possible ways are there to fill the four cells in the bottom row to produce a "+" at the top of the pyramid?[asy]
unitsize(2cm);
path box = (-0.5,-0.2)--(-0.5,0.2)--(0.5,0.2)--(0.5,-0.2)--cycle;
draw(box); label("",(0,0));
draw(shift(1,0)*box); label("",(1,0));
draw(shift(2,0)*box); label("",(2,0));
draw(shift(3,0)*box); label("",(3,0));
draw(shift(0.5,0.4)*box); label("",(0.5,0.4));
draw(shift(1.5,0.4)*box); label("",(1.5,0.4));
draw(shift(2.5,0.4)*box); label("",(2.5,0.4));
draw(shift(1,0.8)*box); label("",(1,0.8));
draw(shift(2,0.8)*box); label("",(2,0.8));
draw(shift(1.5,1.2)*box); label("",(1.5,1.2));
[/asy]