The two pails (5 & 9 quarts) problem

The problem

You have a 5 quart pail and a 9 quart pail and no other way of measuring apart from filling a pail and pouring water from one pail to the other until either the pail being poured into is full or the pail being poured out of is empty. How is it possible to bring back any whole number of quarts, from 1 to 14, with these two containers?

The answer

Action	5q pail	9q pail	Total
Fill 5q pail	5	0	5
Pour all 5q contents into 9q pail	0	5	5
Fill 5q pail	5	5	10
Fill 9q pail from 5q pail	1	9	10
Empty 9q pail	1	0	1

Fill 5q pail	5	0	5
Pour all 5q contents into 9q pail	0	5	5
Fill 5q pail	5	5	10
Fill 9q pail from 5q pail	1	9	10
Empty 9q pail	1	0	1
Pour all 5q contents into 9q pail	0	1	1
Fill 5q pail	5	1	6
Pour all 5q contents into 9q pail	0	6	6
Fill 5q pail	5	6	11
Fill 9q pail from 5q pail	2	9	11
Empty 9q pail	2	0	2

Fill 5q pail	5	0	5
Pour all 5q contents into 9q pail	0	5	5
Fill 5q pail	5	5	10
Fill 9q pail from 5q pail	1	9	10
Empty 9q pail	1	0	1
Pour all 5q contents into 9q pail	0	1	1
Fill 5q pail	5	1	6
Pour all 5q contents into 9q pail	0	6	6
Fill 5q pail	5	6	11
Fill 9q pail from 5q pail	2	9	11
Empty 9q pail	2	0	2
Pour all 5q contents into 9q pail	0	2	2
Fill 5q pail	5	2	7
Pour all 5q contents into 9q pail	0	7	7
Fill 5q pail	5	7	12
Fill 9q pail from 5q pail	3	9	12
Empty 9q pail	3	0	3

Fill 9q pail	0	9	9
Fill 5q pail from 9q pail	5	4	9
Empty 5q pail	0	4	4

Fill 5q pail	5	0	5

Fill 5q pail	5	0	5
Pour all 5q contents into 9q pail	0	5	5
Fill 5q pail	5	5	10
Fill 9q pail from 5q pail	1	9	10
Empty 9q pail	1	0	1
Pour all 5q contents into 9q pail	0	1	1
Fill 5q pail	5	1	6

Fill 5q pail	5	0	5
Pour all 5q contents into 9q pail	0	5	5
Fill 5q pail	5	5	10
Fill 9q pail from 5q pail	1	9	10
Empty 9q pail	1	0	1
Pour all 5q contents into 9q pail	0	1	1
Fill 5q pail	5	1	6
Pour all 5q contents into 9q pail	0	6	6
Fill 5q pail	5	6	11
Fill 9q pail from 5q pail	2	9	11
Empty 9q pail	2	0	2
Pour all 5q contents into 9q pail	0	2	2
Fill 5q pail	5	2	7

Fill 5q pail	5	0	5
Pour all 5q contents into 9q pail	0	5	5
Fill 5q pail	5	5	10
Fill 9q pail from 5q pail	1	9	10
Empty 9q pail	1	0	1
Pour all 5q contents into 9q pail	0	1	1
Fill 5q pail	5	1	6
Pour all 5q contents into 9q pail	0	6	6
Fill 5q pail	5	6	11
Fill 9q pail from 5q pail	2	9	11
Empty 9q pail	2	0	2
Pour all 5q contents into 9q pail	0	2	2
Fill 5q pail	5	2	7
Pour all 5q contents into 9q pail	0	7	7
Fill 5q pail	5	7	12
Fill 9q pail from 5q pail	3	9	12
Empty 9q pail	3	0	3
Pour all 5q contents into 9q pail	0	3	3
Fill 5q pail	5	3	8

Fill 9q pail	0	9	9

Fill 5q pail	5	0	5
Pour all 5q contents into 9q pail	0	5	5
Fill 5q pail	5	5	10

Fill 5q pail	5	0	5
Pour all 5q contents into 9q pail	0	5	5
Fill 5q pail	5	5	10
Fill 9q pail from 5q pail	1	9	10
Empty 9q pail	1	0	1
Pour all 5q contents into 9q pail	0	1	1
Fill 5q pail	5	1	6
Pour all 5q contents into 9q pail	0	6	6
Fill 5q pail	5	6	11

Fill 5q pail	5	0	5
Pour all 5q contents into 9q pail	0	5	5
Fill 5q pail	5	5	10
Fill 9q pail from 5q pail	1	9	10
Empty 9q pail	1	0	1
Pour all 5q contents into 9q pail	0	1	1
Fill 5q pail	5	1	6
Pour all 5q contents into 9q pail	0	6	6
Fill 5q pail	5	6	11
Fill 9q pail from 5q pail	2	9	11
Empty 9q pail	2	0	2
Pour all 5q contents into 9q pail	0	2	2
Fill 5q pail	5	2	7
Pour all 5q contents into 9q pail	0	7	7
Fill 5q pail	5	7	12

Fill 9q pail	0	9	9
Fill 5q pail from 9q pail	5	4	9
Empty 5q pail	0	4	4
Pour all 9q contents into 5q pail	4	0	4
Fill 9q pail	4	9	13

Fill both pails	5	9	14

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