2006 AIME I Problems/Problem 11
Problem
A collection of 8 cubes consists of one cube with edge-length 
for each integer 
A tower is to be built using all 8 cubes according to the rules:
- Any cube may be the bottom cube in the tower.
- The cube immediately on top of a cube with edge-length
must have edge-length at most 
Let 
be the number of different towers than can be constructed. What is the remainder when is divided by 1000?
Solution
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