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 Cover the Center (Posted on 2010-06-04)
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 No Rating

 Subject Author Date re: Four Plank Analysis Dej Mar 2010-06-06 15:49:09 Five and Six Planks Brian Smith 2010-06-05 17:38:43 Four Plank Analysis Brian Smith 2010-06-04 19:13:06 One, Two and Three Planks Brian Smith 2010-06-04 17:34:56 Trying N=4 Jer 2010-06-04 17:14:45 N=2 and N=3 Jer 2010-06-04 16:11:15

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