Difference between revisions of "2002 AIME I Problems/Problem 9"
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== Problem == | == Problem == | ||
| + | Harold, Tanya, and Ulysses paint a very long picket fence. | ||
| + | |||
| + | Harold starts with the first picket and paints every <math>h</math> th picket; | ||
| + | |||
| + | Tanya starts with the second picket and paints every <math>t</math> th picket; and | ||
| + | |||
| + | 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 of positive integers results in every picket being painted exaclty once. Find the sum of all the paintable integers. | ||
== Solution == | == Solution == | ||
Revision as of 15:37, 25 September 2007
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 exaclty once. Find the sum of all the paintable integers.
Solution
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