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More and More Buckets

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

First Andrew,

With $3$ buckets, each holding $4$ litres, there are only four solutions.
$123, 234, 134, 124$

Second Matthew

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 $5$L pails, one $2$L pail, one $6$L pail and two $3$L pails. I put $5$L in one of the $5$L pails and $4$L in the other. I put $2$L in the $2$L one and $6$L in the $6$L one. And for the two $3$L pails, I put $1$L in one and put $3$L 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 how these can all be found by exploring Pascal's Triangle. Well Done.