Difference between revisions of "1997 PMWC Problems/Problem T10"
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==Solution== | ==Solution== | ||
| − | + | The answer is <math>\boxed{0}.</math> | |
| − | + | ||
| + | We first seat <math>1.</math> Then we put all odd numbers in one way and all even numbers in another direction. The result is <math>12,10,8,6,4,2,1,3,5,7,9,11,12...</math> when we read the table. It satisfies the conditions and never has <math>4</math> as a difference. | ||
==See Also== | ==See Also== | ||
{{PMWC box|year=1997|num-b=T9|after=Last<br />Problem}} | {{PMWC box|year=1997|num-b=T9|after=Last<br />Problem}} | ||
Revision as of 16:05, 15 July 2018
Problem
The twelve integers 
are arranged in a circle such that the difference of any two adjacent numbers is either 
or 
. What is the maximum number of the difference can occur in any such arrangement?
Solution
The answer is 
We first seat 
Then we put all odd numbers in one way and all even numbers in another direction. The result is 
when we read the table. It satisfies the conditions and never has as a difference.
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 | ||
