# Liquor distillers of puzzlelandia

Surely everyone knows the problem of the man who had a barrel of honey to sell and who has a three-quart and a five-quart container. The seller meets a customer who wants to buy four quarters of honey exactly. It is simple to transfer the honey with both measures until reaching the required four quarters but exercise the gray matter of their brains and see if they can discover the minimum number of changes with which that problem can be solved.

That well-known problem of leftovers will prepare the mind for our riddle now that consists in discovering how the liquor seller, with two 31-gallon barrels full, one with apple brandy (Apple Jack) and the other with cider (Cider ) You can give your client \$ 21.06 of “Mountain Dew”, which is how the cider and apple brandy mixture is known. The seller has only two measures of 2 and 4 gallons and the customer wants to fill the 26 gallons of his barrel.

Determine first what proportions of cider and brandy give 26 gallons of “Mountain Dew” at an exact cost of \$ 21.06 and then try to discover the least number of manipulations needed to fill the barrel with the indicated amounts.

#### Solution

The old problem of measuring 4 rooms with a measurement of 5 rooms and another of 3 rooms can be solved in 6 movements as follows:

1. Fill the largest measure.
2. Fill the smallest with the big one leaving 2 rooms in the latter.
3. Pour the contents of the small measure back into the barrel.
4. Transfer the two rooms to the small size.
5. Fill the large measure with the barrel.
6. Fill the small measure leaving 4 rooms in the large one. Voilà!

In the second problem, some elemental algebra will tell you that 26 gallons of “Mountain Dew” must contain 24 gallons and 8/17 of apple brandy and 1 gallon and 9/17 of cider to cost \$ 21.06 according to the prices indicated . To measure this mixture as quickly as possible it is necessary to follow the following steps:

1. Fill both measures with apple brandy.
2. Empty the barrel of brandy in the client's barrel.
3. Empty both measures again in the barrel of brandy.
4. Transfer 2 gallons of the client's barrel to the barrel of apple brandy.
5. Transfer 2 gallons of cider from the barrel to the customer's barrel.
6. Fill both measures with the cask mixture. This will leave a mixture containing 1 gallon and 9/17 of cider in the barrel.
7. Fill the customer's barrel with the barrel of apple brandy.