# Solution

(related to Problem: The Honest Dairyman)

Whatever the respective quantities of milk and water, the relative proportion sent to London would always be three parts of water to one of milk. But there are one or two points to be observed. There must originally be more water than milk, or there will be no water in $A$ to double in the second transaction. And the water must not be more than three times the quantity of milk, or there will not be enough liquid in $B$ to effect the second transaction. The third transaction has no effect on $A,$ as the relative proportions in it must be the same as after the second transaction. It was introduced to prevent a quibble if the quantity of milk and water were originally the same; for though double "nothing" would be "nothing," yet the third transaction in such a case could not take place.

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### References

#### Project Gutenberg

1. Dudeney, H. E.: "Amusements in Mathematics", The Authors' Club, 1917

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