Concrete Mathematics Exercise Solution: Chapter 1[problem no: 13].

Question: 1.13: What’s the maximum number of regions definable by zig-zag lines, 

each of which consists of two parallel infinite half-lines joined by a straight segment?

Solution:

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Concrete Mathematics Exercise Solution: Chapter 1[problem no: 11].

Question: 1.11: A Double Tower of Hanoi contains 2n disks of n different sizes, two of each size. As usual, we’re required to move only one disk at a time, without putting a larger one over a smaller one.

1. How many moves does it take to transfer a double tower from one peg to another, if disks of equal size are indistinguishable from each other?
2. What if we are required to reproduce the original top-to-bottom order of all the equal-size disks in the final arrangement? [Hint: This is difficult–it’s really a “bonus problem.”]

Solution:

for a: 

for b: 

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Concrete Mathematics Exercise Solution: Chapter 1[problem no: 2].

Question: 1.2: Find the shortest sequence of moves that transfers a tower of n disks from the left peg A to the right peg B, if direct moves between A and B are disallowed. (Each move must be or to or from the middle peg. As usual, a larger disk must never appear above a smaller one.)

Solution:

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