Jugs of Wine

Problem | Solution | Printable page |
Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

This is a very well-explained solution submitted by Julia (Wymondham High School):


For the jugs holding 9, 7, 4, and 2 litres, this flow diagram shows how the solution can be achieved in three distinct ways, using eight decantings of the wine and, in each case, 9 litres being poured back and forth to achieve the required result.


To measure out all the integer amounts from 1 to 8 litres using three jugs, one of which is full and holds 8 litres, there are several possible solutions. For example, for jugs with capacities 8, 3 and 2 litres, the following triples give the numbers of litres in each of the jugs at successive steps and all the amounts from 1 litre to 8 litres occur at some stage of the process: (8,0,0) (5,3,0) (5,1,2) (7,1,0) (7,0,1) (6,0,2) (6,2,0) (4,2,2). There are other solutions for capacities of 8, 4 and 3; for 8, 5 and 4; for 8, 5 and 1 etc.

 

Two other different students from Wymondham High School, David and Rachel, also submitted good solutions. In their answers, they included a very useful table of results which showed at a glance the state of the jugs after any particular pouring.


Much later two students from Flegg High, Luke and Ian, also submitted a successful solution to this problem. They had found their answer after "hours of trouble, and help from Mrs Fenn".



Published October 1997.