Measuring water

"I suggest the problem is so poorly defined that any answer could be correct."

Roger, I suggest you think about it a little more. C'mon! Work that big brain!

General solution:

1. 1 cup from wine bucket A (quantity >= 1 cup) is added to water bucket B (quantity n cups, n>=1):

2. B has n+1 cups mix: n cups water, 1 cup wine.

3. Filling 1 cup from B thus gives a mixture of n/(n+1) cups water and 1/(n+1) cups wine.

4. B, after the cup is taken back, has the original 1 cup of wine, less the amount in the cup going back to A, or 1-[1/(n+1)] cups wine. This simplifies to n/(n+1) as per (3).

5. A, with its n/(n+1) cups water from the mixed cup from B, thus has the same amount of water as there is wine in B.

That's a lot of math for a simple question….

Wine being mostly water by composition, both buckets contain mostly water no matter what you do with them!

Also, in regards to "eyeballing it"…the one area I've found not to do this is in making coffee for a group. Get it right, then replicate exactly every day.

I concur with Jeremy that (if the buckets are larger than cups (a reasonable assumption) and the two buckets are the same size/fullness at the start, then) there is exactly as much water in the wine as wine in the water after the two transfers, regardless of the size of the cups.

Nice problem. I use it at Middle School Math Club tomorrow.

Nobody mentioned paint pens as a good marking tool. They last MUCH longer than a sharpie and easier to do than dremel or punch marks. Available at hobby lobby or art stores for $3-4.