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Involve the reve's puzzle, the variation of the tower of hanoi puzzle with four pegs and n disks. Before presenting these exercises, we describe the Frame-Stewart algorithm for moving the disks from peg 1 to peg 4 so that no disk is ever on top of a smaller one. This algorithm, given the number of disks n as input, depends on a choice of an integer k with 1 ≤ k ≤ n. When there is only one disk, move it from peg 1 to peg 4 and stop. For n > 1, the algorithm proceeds recursively, using these three steps. Recursively move the stack of the n - k smallest disks from peg 1 to peg 2, using all four pegs. Next move the stack of the k largest disks from peg 1 to peg 4, using the three-peg algorithm from the Tower of Hanoi puzzle without using the peg holding the n - k smallest disks. Finally, recursively move the smallest n - k disks to peg 4, using all four pegs. Frame and Stewart showed that to produce the fewest moves using their algorithm, k should be chosen to be the smallest integer such that n does not exceed tk = k(k + 1)/2, the kth triangular number, that is, tk-1
Use Exercise 43 to give an upper bound on the number of moves required to solve the Reve's puzzle for all integers n with 1 ≤ n ≤ 25.
After 10 hours of radiation decay 50mg of a substance remains. After 15 hours 30mg remained.
find an equation of the tangent linr to the curve at the given point y=2x^3-5x at the point (-1,3)
What is the probability that a freshman selected at random from this group is enrolled in each of the following? (Enter your answers to three decimal places.)
The probability that both defective lights will be found, A box contains two defective Christmas tree lights that have been inadvertently mixed with eight non-defective lights. If the lights are selected one at a time without replacement
A plane has an airspeed of 195 miles per hour and a heading of 20°. The ground speed of the plane is 207 miles per hour, and its true course is in the direction of 36°. Find the speed and direction of the air currents, assuming they are constants.
What is the total defect rate? I came up with 6%. A randomly selected product was defective. What is the probability that it came from Plant A?
Construction A bu ildi ng foundation has a length of 82 ft and a perimeter of 292 ft. What is the width? (H int: Peri meter = 2 X length + 2 X width.)
Maria went to the ladies fashion store and bought a dress on sale at 120.95. the dress reduced an extra 15% off What was the total price of the dress including 12% tax?
Carol sells two types of PC monitors. She sold a total of 14 monitors last month. One model sells for $280 and the other sells for $435. If the total sales for the 14 monitors was $5,160, determine the number of each type of monitor she sold.
A Chemist needs 100 milliliters of a 76% solution but has only 55% and 85% solutions available. Find how many milliliters of each that should me mixed to get the desired soultion?
Math 104: Homework 3. Let (sn) and (tn) be Cauchy sequences defined on R, and let (un) be a sequence defined as un = asn + btn for all n, where a, b ∈ R. By using the definition of a Cauchy sequence only, without assuming that limits of (sn) and (tn)..
Write down 2 equations to compute a and P, one when t=2 and the other when t= 6.
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