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Cover the Center (Posted on 2010-06-04) Difficulty: 5 of 5
Can you cover the center of a unit circle, such a Indi's circular pit?

You have a number (N) of identical planks of length L (0 < L <= 2). The planks have small width and negligible thickness, but very high strength and rigidity. No plank extends outside the circle. Both endpoints of each plank, with the exception of the N-th plank, must rest on either the circle or another plank. Neither weaving of planks nor cantilever designs are allowed. Covering the center means that the N-th plank crosses over the center of the circle.

For a given N, L is the minimum length plank necessary.
Obviously if N=1, then L=2.

What is the smallest L when N=2? N=3? N=4?

For larger N, is there an optimum algorithm to minimize L?

Can you determine a general relationship between N and L?

No Solution Yet Submitted by Larry    
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  Subject Author Date
Some Thoughtsre: Four Plank AnalysisDej Mar2010-06-06 15:49:09
Some ThoughtsFive and Six PlanksBrian Smith2010-06-05 17:38:43
Some ThoughtsFour Plank AnalysisBrian Smith2010-06-04 19:13:06
Some ThoughtsOne, Two and Three PlanksBrian Smith2010-06-04 17:34:56
Trying N=4Jer2010-06-04 17:14:45
Some ThoughtsN=2 and N=3Jer2010-06-04 16:11:15
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