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Kenneth Rosen Edition 7 Exercise 8.1 Question 1 (Page No. 510)
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Use mathematical induction to verify the formula derived in Example $2$ for the number of moves required to complete the Tower of Hanoi puzzle.
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Kenneth Rosen Edition 7 Exercise 8.1 Question 7 (Page No. 510 - 511)
Find a recurrence relation for the number of bit strings of length $n$ that contain a pair of consecutive $0s$. What are the initial conditions? How many bit strings of length seven contain two consecutive $0s?$
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Kenneth Rosen Edition 7 Exercise 8.1 Question 6 (Page No. 510)
Find a recurrence relation for the number of strictly increasing sequences of positive integers that have 1 as their first term and n as their last term, where n is a positive integer. That is, sequences $a_{1}, a_{2},\dots,a_{k},$ ... How many sequences of the type described in $(A)$ are there when $n$ is an integer with $n \geq 2?$
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Kenneth Rosen Edition 7 Exercise 8.1 Question 5 (Page No. 510)
How many ways are there to pay a bill of $17$ pesos using the currency described in question $4,$ where the order in which coins and bills are paid matters?
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Kenneth Rosen Edition 7 Exercise 8.1 Question 4 (Page No. 510)
A country uses as currency coins with values of $1$ peso, $2$ pesos, $5$ pesos, and $10$ pesos and bills with values of $5$ pesos, $10$ pesos, $20$ pesos, $50$ pesos, and $100$ pesos. Find a recurrence relation for the number of ways to pay a bill of $n$ pesos if the order in which the coins and bills are paid matters.
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