Ralph’s Puzzle

This puzzle happens to be set in an English tavern in olden times. Two regular customers, Samuel and Ezra, ask Ralph, the landlord, for a pint of beer each.

Ralph’s problem is that he has three measures but they are eight-gill, five-gill and three-gill (remembering that a gill is a quarter of a pint). However being a resourceful man and keen not to lose a sale he finds a way to satisfy his customers. Can you work out how he did it?

To begin with he draws eight gills from the barrel filling the largest measure.

Let’s call the measures

           A                          B                          C

He decides to pour the beer from measure to measure until he has 4 gills ( a pint) of beer in each of the larger measures. But what is the smallest number of pourings needed to do the job?

To write it down you could start with 8 + 0 + 0, then 3 + 5 + 0 after the first pouring from A to B (big clue here) and so on. When you have worked it out you can see the shortest answer step by step here.

Pouring 1.    A > B gives 3+5+0

Pouring 2.    B > C gives 3+2+3

Pouring 3.    C > A gives 6-2-0

Pouring 4.    B > C gives 6+0+2

Pouring 5.    A > B gives 1+5+2
Note: 1 gill is left in measure A

Pouring 6.    B > C gives 1+4+3
Note: 1 gill to fill C leaves 4 gills in B

Pouring 7.    C > A gives 4+4+0 (1 pint+1 pint)

It takes seven pourings from measure to measure
to solve the puzzle and give Samuel and Ezra
their pints of beer.