Task 461

The task

Three dice with faces numbered 1 through 6 are stacked as shown. Seven of the eighteen faces are visible, leaving eleven faces hidden(back, bottom, between). What is the total number of dots NOT visible in this view? [asy] /* AMC8 2000 #8 Problem */ draw((0,0)--(1,0)--(1.5,0.66)--(1.5,3.66)--(.5,3.66)--(0,3)--cycle); draw((1.5,3.66)--(1,3)--(1,0)); draw((0,3)--(1,3)); draw((0,1)--(1,1)--(1.5,1.66)); draw((0,2)--(1,2)--(1.5,2.66)); fill(circle((.75, 3.35), .08)); fill(circle((.25, 2.75), .08)); fill(circle((.75, 2.25), .08)); fill(circle((.25, 1.75), .08)); fill(circle((.75, 1.75), .08)); fill(circle((.25, 1.25), .08)); fill(circle((.75, 1.25), .08)); fill(circle((.25, 0.75), .08)); fill(circle((.75, 0.75), .08)); fill(circle((.25, 0.25), .08)); fill(circle((.75, 0.25), .08)); fill(circle((.5, .5), .08)); /* Right side */ fill(circle((1.15, 2.5), .08)); fill(circle((1.25, 2.8), .08)); fill(circle((1.35, 3.1), .08)); fill(circle((1.12, 1.45), .08)); fill(circle((1.26, 1.65), .08)); fill(circle((1.40, 1.85), .08)); fill(circle((1.12, 1.85), .08)); fill(circle((1.26, 2.05), .08)); fill(circle((1.40, 2.25), .08)); fill(circle((1.26, .8), .08)); [/asy]