Difference between revisions of "2006 AIME I Problems/Problem 11"
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Let <math> T </math> be the number of different towers than can be constructed. What is the remainder when <math> T </math> is divided by 1000? | Let <math> T </math> be the number of different towers than can be constructed. What is the remainder when <math> T </math> is divided by 1000? | ||
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== Solution == | == Solution == | ||
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== See also == | == See also == | ||
| − | * [[2006 AIME I]] | + | * [[2006 AIME I Problems]] |
Revision as of 11:14, 30 June 2006
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?
