Category Archives: MATH 233

MATH 233 Week 6 Homework Exercises Updated

MATH 233 Week 6 Homework Exercises Updated

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MATH 233 Week 6 Homework Exercises Updated

7.5 #2

Two friends have 2 gallons (8 quarts) of water in a pail. They also have two (empty) jars, one holding 5 quarts and the other 3. Using just these measuring devices, how can they split the water so that 4 quarts are in the larger jar and 4 quarts remain in the pail? Produce a complete graph model for this puzzle similar to the one in the wolf, goat, and cabbage puzzle, and find all solutions to the water puzzle in terms of the properties of the graph.

7.5 #4

Puzzles like the wolf, goat, and cabbage puzzle exist in many cultures (see [2]). A slightly different version comes from the Kabjlie region of Algeria. This puzzle involves a man traveling with a jackal, a goat, and a bundle of hay, but in this version, the man can take up to two of these things with him on each crossing. Describe the complete graph model so that you can show all the solutions to this puzzle in terms of your graph. Is there a solution that seems to be better than others? Explain why.

7.5 #10

Suppose two players play a game with two piles of stones (initially with seven stones in each pile) and the rule that on a given turn it is permissible to remove up to three stones total on each turn, but at least one stone must be removed from each pile if possible. Find the kernel, and decide which player has a winning strategy in this game.

7.6 #4

Place the numbers 11, -4, 3, 2, 16, 8, 5, -1 into a binary search tree with the smallest possible height.

7.6 #6c & 6d

Give the binary tree that represents each of the following “inorder” arithmetic expressions:

(c) (((3+5)-7) x 4) / 2