MathDB

A collection of 8 cubes consists of one cube with edge-length

k

for each integer

k,\thinspace 1 \le k \le 8.

A tower is to be built using all 8 cubes according to the rules:

\bullet

Any cube may be the bottom cube in the tower.

\bullet

The cube immediately on top of a cube with edge-length

k

must have edge-length at most

k+2.

Let

T

be the number of different towers than can be constructed. What is the remainder when

T

is divided by 1000?

Problem Statement