QOD #30 — Solution

Solution

What, in fact, happened was that Le poured out 7 pitchers of the 7 quart jug (49 quarts) onto the rug in front of the TA office. She then proceeded to dump out 14 pitchers using the 5 quart jug (70 quarts). All together, she dumped out 119 quarts of water, and then poured the remaining one quart for herself.

Comments

Great answer!

Of course, if Gary lets Le dump the water (in an approved container), getting one quart is easy:

Cooler	7-quart jug	5-quart jug	Action
120	0	0	Initial conditions
113	7	0	Fill the 7
113	2	5	Transfer as much as possible from the 7 to the 5
106	7	2	Dump the 5, transfer the 7 to the 5, and fill the 7
106	4	5	Transfer as much as possible from the 7 to the 5
99	7	4	Dump the 5, transfer the 7 to the 5, and fill the 7
99	6	5	Transfer as much as possible from the 7 to the 5
99	1	5	Dump the 5, and transfer as much as possible from the 7 to the 5
99	1	0	Dump the 5

Since I just took about five minutes to figure that out, someone tell me if they have a better answer (i.e. one that wastes less water)

Henry says: Isn't the point to dump as much water as possible? Revenge on GaryTA! Muahahaha! Or, if you want to be boring and conserve water, how 'bout--

fill 5 | pour 5 into 7 | fill 5 | pour 5 into 7, leaving 3q in 5 | dump 7 | pour 5 in 7 (3q) | fill 5 | pour 5 into 7, leaving 1q in 5. Done.

That works, right?

Cooler	7-quart jug	5-quart jug	Action
120	0	0	Initial conditions
115	0	5	Fill the 5
110	5	5	Transfer the 5 to the 7, and fill the 5
110	7	3	Transfer as much as possible from the 5 to the 7
105	3	5	Dump the 7, transfer the 5 to the 7, and fill the 5
105	7	1	Transfer as much as possible from the 5 to the 7
105	0	1	Dump the 7

Okay, so that saves six quarts. Good for you, Henry.

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