Difference between revisions of "2002 AIME I Problems/Problem 9"

(Problem)
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== Problem ==
 
== Problem ==
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Harold, Tanya, and Ulysses paint a very long picket fence.
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Harold starts with the first picket and paints every <math>h</math> th picket;
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Tanya starts with the second picket and paints every <math>t</math> th picket; and
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Ulysses starts with the third picket and paints every <math>u</math> th picket.
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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 16:37, 25 September 2007

Problem

Harold, Tanya, and Ulysses paint a very long picket fence.

Harold starts with the first picket and paints every $h$ th picket;

Tanya starts with the second picket and paints every $t$ th picket; and

Ulysses starts with the third picket and paints every $u$ th picket.

Call the positive integer $100h+10t+u$ 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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See also