Difference between revisions of "1997 PMWC Problems/Problem T10"

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==Problem==
 
==Problem==
 
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The twelve integers <math>1, 2, 3,\dots, 12</math> are arranged in a circle such that the difference of any two adjacent numbers is either <math>2, 3,</math> or <math>4</math>. What is the maximum number of the difference <math>4</math> can occur in any such arrangement?
The twelve integers 1, 2, 3,..., 12 are arranged in a circle such that the difference of any two adjacent numbers is either 2, 3 or 4. What is the maximum number of the difference '4' can occur in any such arrangement?
 
  
 
==Solution==
 
==Solution==

Revision as of 13:44, 20 April 2014

Problem

The twelve integers $1, 2, 3,\dots, 12$ are arranged in a circle such that the difference of any two adjacent numbers is either $2, 3,$ or $4$. What is the maximum number of the difference $4$ can occur in any such arrangement?

Solution

Less than 9. This problem needs a solution. If you have a solution for it, please help us out by adding it.

See Also

1997 PMWC (Problems)
Preceded by
Problem T9
Followed by
Last
Problem
I: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
T: 1 2 3 4 5 6 7 8 9 10