Friday Puzzle -- Wine Pouring

Wine Pouring time for a hint

Alex Y

This wine is not aging well!

Here are a couple of hints that might prove helpful.

At the end, one of the large vessels is full and the other has 4 quarts of wine.

The four quart container after every pour is either full, empty, or contains three quarts. And once it has three quarts, it is never poured to or from again.

Re: Friday Puzzle -- Wine Pouring

Henry Higginbotham

Can the solution involve a female companion and a bit of imbibing any time there's an inconvenient quart left in a container?

Re: Friday Puzzle -- Wine Pouring

Alex Y

Well, in the statement of the problem, I did say that no wine could be wasted, and I'm sure you'd argue that your plan is not a waste of wine . But, no, that is not the intent.

A start, maybe ...

Larry Barrett

10 10 4 5

--- --- -- --

10 10 0 0

10 6 4 0

10 6 0 4

10 2 4 4

10 2 3 5

This gets the 4 container filled with 3 qts, but the next move (pouring the 5 qts from the 5 container back into the 10 container, filling it to 7 qts, seems to lead nowhere.

Wine Pouring -- a bigger hint

Alex Y

There are 11 pours required to get the measures sought. They are best described in a table of the states of each container after each pour. i.e., pour one takes the containers from state 0 to state 1. Here is that table with a few boxes filled in:



State 8 is the first time that the 4 quart vessel has exactly 3 quarts of wine. From that, you can determine what state 7 looked like. Also, from the fact that state 10 was not a solution, you can narrow down state 10 to two possibilities, one of which you will be able to rule out when trying to get a state 9 that works with both 8 and 10.

Good luck. This is the hardest "pouring" puzzle I have seen. Most are just three vessels that get to be easy once you have done a few.

Re: Wine Pouring -- a bigger hint

Larry Barrett

I think the 4 container contains these amounts in steps 0 through 11:

0 4 4 0 4 4 0 4 3 3 3 3

Re: Wine Pouring -- a bigger hint

Alex Y

Interesting. I'll look forward to comparing solutions. The solution I have seen has 0 in the 4-qt container after the first pour, but the rest is identical to yours, at least with that container. But it is easy to see that these two solutions diverge pretty much in the first few turns. I wonder if they keep on different paths until pour 8 (I suspect they do) or come back to the same moves sooner than that.

Re: Wine Pouring -- a bigger hint

Larry Barrett

I double checked and think my solution is correct. Steps 1 and 2 are interchangeable in this solution; if I had started with step 2 then the contents of container 4 would start (from step 0) this way: 0 0 4 0 4 4 0 ...

Re: Wine Pouring -- a bigger hint

Keith Weber

Here's what I would do...

It takes me 4 pours to get 3 quarts into the 4-quart container. I'd then empty the 5 quart container back into the 10-quart container, so I'd have 10-7-0-3. I'd then mark the 4-quart container, so I'd know where 3 quarts is, and then empty it into the 5-quart container, giving me 10-7-3-0. Now fill the fill the 4-quart container to the mark from the 10-quart container. 7 pours gives me 7-7-3-3. Then I'd invite some friends over to drink the extra 14 quarts so that none is wasted.

Keith