Hints for Puzzle 51:

Suppose you had two glasses with capacities of 5 oz. and 8 oz., and you need to measure off exactly 6 oz. from the 24 oz. vase.

Notice that if you fill the 8 oz. glass and then pour off 5 oz. into the 5 oz. glass you will have 3 oz. left.

Pour the 5 oz. back into the vase and pour the 3 oz. left into the 5 oz. glass.

Now repeat, fill the 8 oz. glass and pour off as much as possible into the 5 oz. glass. Since it already has 3 oz. in it you can only pour in 2 oz., leaving exactly 6 oz. in the 8 oz. glass!