有沒有好辦法？

來源: cma 於 2012-01-25 21:15:23 [檔案] [舊帖] [給我悄悄話] 閱讀數 : (11326 bytes)

$2006$ 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.