I caught this good one while I was having a leisurely look at mayhem taunt problems (M74).May look daunting at the first but you should be able to hit it within 10 minutes.
Problem: A circle has 12 equally spaced points on its circumference. How many ways can the numbers 1 through 12 be assigned to the points so that if the points 1 through 12 are connected with line segments, in order, the segments do not cross ? an bad example is here.[S]
1 comment:
Place points 1 and 2 arbitrarily on two distinct places on the circumference of the circle. This divides the circumference into two parts, mark them A1 and B1 for convenience. Point 3 can be either placed in A1 or B1.Once 3 is placed in one of the region (say A1), then following points cannot be placed in the other.3 divides the region (here A1) into two parts again, where 4 can be placed and so on.
Hence there are 2^[12-2] =1024 ways.
Please comment back if you need any more clarification on the solution.
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