Well done to everyone who engaged themselves in this challenge. Here are just some of the solutions we had emailed to us. Eskdale School sent in two solutions that I'm showing here.
With 3 buckets, each holding 4 litres, there are only four solutions.
123, 234, 134, 124
If we are only allowed to use four numbers out of five, then we must leave out one number. Once we have used our numbers there is always one left. There are five numbers to pick out of. So there are five possibilities.
James, from St. John French Immersion School in Ontario sent in this good one (and like Jack and Gill that went up the hill he used pails instead of buckets):
I took two 5L pails, one 2L pail, one 6L pail and two 3L pails. I put 5L in one of the 5L pails and 4L in the other. I put 2L in the 2L one and 6L in the 6L one. And for the two 3L pails, I put 1L in one and put 3L in the other.
Rajeev from Fair Field School sent in some very thorough thoughts and ideas as follows:
6 litres and 5 buckets would have a combination of 6
6 litres and 4 buckets would have a combination of 15
7 litres and 6 buckets would have a combination of 7
7 litres and 5 buckets would have a combination of 21
7 litres and 4 buckets would have a combination of 35
7 litres and 3 buckets would have a combination of 35
7 litres and 2 buckets would have a combination of 21
7 litres and 1 buckets would have a combination of 7
and with 12 litres and 6 buckets it would be 924
and with 13 litres and 6 buckets it would be 1716
He also showed here.doc or here.pdf how these can all be found by exploring Pascal's Triangle. Well Done.