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Find a recurrence relation for the number of ways to go n miles by foot walking at 2 miles per hour or jogging at 4 miles per hour or running at 8 miles per hour or running at 8 miles per hour, at the end of each hour a choice is made of how to go the next hour. How many ways are there to go 12 miles? Find a recurrence relation for the number of ways to distribute a total of n cents on successive days using 1971 pennies, 1951 nickels, 1967 nickels, 1959 dimes, and 1975 quarters. Find a recurrence relation for the number of n-digit binary sequences with no pair of consecutive 1s. Repeat for n-digit ternary sequences. Repeat for n-digit ternary sequences with noconsecutive Is or consecutive 2s. Find a recurrence relation for the number of pairs of rabbits after n months it initially there is one pair of rabbits who were just born, and every month each pair of rabbits that are over one month old have a pair of offspring (a male and a female).

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