Difference between revisions of "2002 AIME I Problems/Problem 9"
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Ulysses starts with the third picket and paints every <math>u</math> th picket. | Ulysses starts with the third picket and paints every <math>u</math> th picket. | ||
| − | Call the positive integer <math>100h+10t+u</math> paintable when the triple <math>(h,t,u)</math> of positive integers results in every picket being painted | + | Call the positive integer <math>100h+10t+u</math> paintable when the triple <math>(h,t,u)</math> of positive integers results in every picket being painted exactly once. Find the sum of all the paintable integers. |
== Solution == | == Solution == | ||
Revision as of 09:20, 5 May 2008
Problem
Harold, Tanya, and Ulysses paint a very long picket fence.
Harold starts with the first picket and paints every 
th picket;
Tanya starts with the second picket and paints every 
th picket; and
Ulysses starts with the third picket and paints every 
th picket.
Call the positive integer 
paintable when the triple 
of positive integers results in every picket being painted exactly once. Find the sum of all the paintable integers.
Solution
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See also
| 2002 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 8 |
Followed by Problem 10 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
