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Unformatted text preview: = c(2n) and Pn + qn = c(2n) 1. Since al = 1, C(21)  1 = 1 and c = 1. We obtain an = 2 n 1. (d) If n = 8, we require 2 8 1 = 255 seconds ~ 4 minutes. If n = 16, we require 2 16 1 = 65535 seconds ~ 18 hr If n = 32, we require 2 32 1 = 4294967295 sec ~ 136 yrs. If n = 64, we require 2 64 1 sec ~ 5.8 x 1011 yr. 24. (a) Labelling the pegs A, B and C and numbering the disks 1,2, ... , n here is a solution for n = 2 with the tower initially on peg A (* denotes no disks). A B C Initial position 1,2 * * Four moves are required. By reversing these steps, we Move 1 2 1 * see that four moves also suffice when the tower is iniMove 2 2 * 1 tially on the middle peg. Move 3 * 2 1 Move 4 * 1,2 * Here is a solution for n = 3, again assuming that the tower is initially on peg A....
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 Summer '10
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 Graph Theory

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