You have three cups which differ in volume and shape. You know that the largest cup is less than three times the volume of the smallest cup. Each cup has a mark showing how much one-third is. You also have a drain.

The largest cup is already full of water. Pour water back and forth to fill all three cups to their one-third mark, pouring any excess down the drain.

Note: If a cup is less than one third filled, it may be filled up to the one third line BUT if a cup is over one third full it cannot be poured out to reduce it to exactly one third filled because when the cup is tipped, you have no indicator for one third full when tipped.

Ok, first notice that we are given a drain, but no mention of a sink. So we can’t rely on a sink. So we better be sure that we have enough water. While I know this isn’t "legal," the limit of the maximum volumes for A, B, and C are that C = 3A, and B = C. So the total amount of water needed is A/3 + B/3 + C/3 = (A+B+C)/3 = (C/3+C+C)/3 = 2.33333/3 * C. This will always be less than C, and since we start out with C being full of water, we know we will have enough water.

Since we can’t simply fill A to 1/3, then fill B to 1/3, and then pour out C until 1/3, we must have another scheme. What we have to do is have a third of two cups being held in ONE cup. Then the other two cups can figure out the other third, dump the excess, and then the ONE cup can pour its correct volumes out. I hope that made sense.

Well, I could pour from C to A up to the 1/3 line. Then I could pour from C to B up to the 1/3 line. Then I empty A into B. I know I can do this because B>A, so even if B = A, I know that B could hold B/3 + A/3.

Then I pour from C to A, filling A. If there is anything in C, I dump it.

Then I pour from A to C up to the 1/3 line. I know I can do this because we are told that C < 3A, which means that A > C/3. So A will be enough to fill C to the 1/3 line.

I dump out whatever is left in A. Then I can pour from B to A up to the 1/3 line. Because of the way I filled B, this will automatically leave B with 1/3 of water.

Posted by nikki on 2004-10-25 19:42:34