Task 1154

The task

A wooden block is 4 inches long, 4 inches wide, and 1 inch high. The block is painted red on all six sides and then cut into sixteen 1 inch cubes. How many of the cubes each have a total number of red faces that is an even number? [asy] size(4cm,4cm); pair A,B,C,D,E,F,G,a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r; A=(0.5,0.1); B=(0.5,0); C=(0,0.5); D=(1,0.5); E=C+(D-A); F=C+(B-A); G=D+(B-A); draw(A--D--E--C--A--B--G--D); draw(C--F--B); a=(3/4)*F+(1/4)*B; b=(1/2)*F+(1/2)*B; c=(1/4)*F+(3/4)*B; m=(3/4)*C+(1/4)*A; n=(1/2)*C+(1/2)*A; o=(1/4)*C+(3/4)*A; j=(3/4)*E+(1/4)*D; k=(1/2)*E+(1/2)*D; l=(1/4)*E+(3/4)*D; draw(a--m--j); draw(b--n--k); draw(c--o--l); f=(3/4)*G+(1/4)*B; e=(1/2)*G+(1/2)*B; d=(1/4)*G+(3/4)*B; r=(3/4)*D+(1/4)*A; q=(1/2)*D+(1/2)*A; p=(1/4)*D+(3/4)*A; i=(3/4)*E+(1/4)*C; h=(1/2)*E+(1/2)*C; g=(1/4)*E+(3/4)*C; draw(d--p--g); draw(e--q--h); draw(f--r--i); [/asy]