# The jigsaw puzzles

Of course we all know the problem of the man who had a barrel of honey to sell and encounters a customer who owns a three-quart and a five-quart container, and who wants to buy four quarts of honey. It is simple to transfer the honey with both measures until you reach the required four quarters, but exercise the gray matter of your brains and see if you can discover how few changes that problem can be solved.

That well-known problem will prepare the mind for our riddle now, which consists in discovering how the liquor store, with a barrel of apple brandy and another one of cider (31 gallons each barrel) can give its client \$ 21.06 of “ Mountain Dew ”, which is what they call the cider and apple brandy mixture. The liquor store has only the measures of 2 and 4 gallons, and the client wishes 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, then try to discover the least number of manipulations that must be done to fill the barrel with the required quantities.

#### Solution

The old problem of measuring 4 rooms with a measure of 5 rooms and one of 3 rooms can be solved in 6 movements:

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 in the barrel.
6. Fill the small measure leaving 4 rooms in the large one.

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 based on prices dices. 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 barrel with the barrel of apple brandy.