有沒有好辦法？

來源: 於 2012-01-25 21:15:23 [舊帖] [給我悄悄話] 本文已被閱讀：次

2006 colored beads are placed on a necklace (circular ring) such that each bead is adjacent to two others. The beads are labeled a_0, a_1, \ldots, a_{2005} around the circle in order. Two beads a_i and a_j, where i and j are non-negative integers, satisfy a_i = a_j if and only if the color of a_i is the same as the color of a_j. Given that there exists no non-negative integer m < 2006 and positive integer n < 1003 such that a_m = a_{m-n} = a_{m+n}, where all subscripts are taken \pmod{2006}, find the minimum number of different colors of beads on the necklace.

先在此謝過。