一条闭串项链由35颗珠子组成，珠子的颜色共分7种。从7种颜色中选3种共有35种不同组合。请找出一种珠子安排，令这35种不同颜色组合在项链的每3颗相连珠子中恰好出现1次。
英文原文
Ponder This Challenge:
Puzzle for January 2005
Our New Years puzzle was submitted by John G. Fletcher,
who heard it from Marc Roth.
A necklace is made up of 35 beads forming a closed loop, each bead being of one of 7 distinct colors. Find an arrangement for the beads such that every one of the 35 combinations of the 7 colors taken 3 at a time occurs exactly once as a set of 3 consecutive beads.
The first 100 people who answer correctly will be listed. The answer will be posted a week after the 100th is received, or at the end of the month.
This problem is not easy, as there is no general rule to solve it. Some people who successfully solved the problem used computer. I was wondering whether any algorithm for Halmiton cycles can help. --This problem can be viewed as a variant of /halmiton cycle, I think. |
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