Difference between revisions of "Mock AIME 5 2005-2006 Problems/Problem 15"
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== Problem == | == Problem == | ||
| + | <math>2006</math> colored beads are placed on a necklace (circular ring) such that each bead is adjacent to two others. The beads are labeled <math>a_0</math>, <math>a_1</math>, <math>\ldots</math>, <math>a_{2005}</math> around the circle in order. Two beads <math>a_i</math> and <math>a_j</math>, where <math>i</math> and <math>j</math> are non-negative integers, satisfy <math>a_i = a_j</math> if and only if the color of <math>a_i</math> is the same as the color of <math>a_j</math>. Given that there exists no non-negative integer <math>m < 2006</math> and positive integer <math>n < 1003</math> such that <math>a_m = a_{m-n} = a_{m+n}</math>, where all subscripts are taken <math>\pmod{2006}</math>, find the minimum number of different colors of beads on the necklace. | ||
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| + | == Solution == | ||
== Solution == | == Solution == | ||
Latest revision as of 21:20, 8 October 2014
Contents
Problem
colored beads are placed on a necklace (circular ring) such that each bead is adjacent to two others. The beads are labeled 
, 
, 
, 
around the circle in order. Two beads 
and 
, where 
and 
are non-negative integers, satisfy 
if and only if the color of is the same as the color of . Given that there exists no non-negative integer 
and positive integer 
such that 
, where all subscripts are taken 
, find the minimum number of different colors of beads on the necklace.
Solution
Solution
See also
| Mock AIME 5 2005-2006 (Problems, Source) | ||
| Preceded by Problem 14 |
Followed by Problem 15 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
