rs a fence with a stile er. She and the dogs needto A dog owner walking her thre
ID: 3148246 • Letter: R
Question
rs a fence with a stile er. She and the dogs needto A dog owner walking her three dogs (Fido, Rover, and Spot) in the countryside enounte cross the fence to the next pasture, however, the dogs will not multiple trips from one side of the fence to the other. Moreover, she can't leave (since Spot plays too rough with Rover) and she can't leave Fido and Rover along together (since they like to run off together to find smelly stuff to roll in). limb the stile so she needs to carry them over, one at a time, making Rover and Spot alone together on one side of the fence We can describe each state by listing who is on each side of the fence. For example, we can use the pair (OR, FS) for the state where owner and Rover are on one side of the fence and Fido and Spot are on the other side. The empty set symbol is used when nothing is on a side, so that (OFRS) is the initial state. a. Find all the allowable states of the puzzle, where neither Rover and Spot nor Fido and Rover are left on the same side of the fence without their owner. b. Construct a graph such that each vertex of this graph represents an allowable state and the vertices representing two allowable states ected by an edge if it is possible to more from one state to the other using one trip over the stile c. Explain why finding a path from the vertex representing (OFRS, o) to the vertex representing (o, OFRS) solves the d. Find two different solutions of the puzzle, each using seven crossings. ighs 12 bs, Rover weighs 17 lbs, and Spot weighs 33 lbs. Which solution of the puzzle results in a smaller total weight carried by the owner over the course the seven crossings?
Explanation / Answer
d)first solution-
OR|FS
R|OFS
ORF|S
F|ORS
OFS|R
FS|OR
OFRS|xxxxxx
SECOND SOLUTION WILLL BE
OR|FS
R|OFS
ORS|F
S|ORF
OFS|R
FS|OR
OFSR|XXXX
e)as you can observe in both methods owner has to carry same weight
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