Liquid Pouring Puzzles 151- PROHIBITION AGAIN
Let us now try to discover the fewest possible manipulations under the same
conditions as in the last puzzle, except that we may now pour back into the
barrel.
- THE KEG OF WINE
A man had a IO-gailon keg of wine and a jug. One day he drew off a jugful
of wine and filled up the keg with water. Later on, when the wine and water
had got thoroughly mixed, he drew off another jugful, and again filled up the
keg with water. The keg then contained equal quantities of wine and water.
What was the capacity of the jug?- WATER MEASUREMENT
A maid was sent to the brook with two vessels that exactly measured 7 pints
and II pints respectively. She had to bring back exactly 2 pints of water.
What is the smallest possible number of transactions necessary? A "transac-
tion" is filling a vessel, or emptying it, or pouring from one vessel to another.408. MIXING THE WINE
A glass is one-third full of wine, and another glass, with equal capacity, is
one-fourth full of wine. Each is filled with water and their contents mixed in
a jug. Half of the mixture is poured into one of the glasses. What proportion
of this is wine and what part water?409. THE STOLEN BALSAM
Three men robbed a gentleman of a vase containing 24 ounces of balsam.
While running away, they met in a forest a glass seller, of whom, in a great
hurry, they purchased three vessels. On reaching a place of safety they
wished to divide the booty, but they found that their vessels contained 5, II,
and 13 ounces respectively. How could they divide the balsam into equal
portions?