Henry Ernest Dudeney/Modern Puzzles/183 - At the Brook

Modern Puzzles by Henry Ernest Dudeney: $183$

At the Brook

In introducing liquid measuring puzzles in my book Amusements in Mathematics, I have said,

"It is the general opinion that puzzles of this class can only be solved by trial,

but I think formulæ can be constructed for the solution generally of certain related cases.

It is a practically unexplored field for investigation."

So far as I know, the hint has not been taken and the field is still unexplored,

so I recently took advantage of a little unexpected leisure to look into the matter.

The result, as I thought probable, was that I struck some new and very interesting things.

Let us take the simplest possible case of a man who goes to a brook with only two vessels with which to measure a given quantity of water.

When we are dealing, say, with a barrel of wine we may have complications arising from the barrel being full or empty,

from its capacity and contents being known or unknown,

from waste of wine being permitted or not permitted,

and from pouring back into the barrel being allowed.

All these points are eliminated.

Is it then possible that any puzzle remains? Let us see.

A man goes to the brook with two measures of $15$ pints and $16$ pints.

How is he to measure exactly $8$ pints of water, in the fewest possible transactions?

Filling or emptying a vessel or pouring any quantity from one vessel to another counts as a transaction.

The puzzle is not difficult, but I think the reader will find it very entertaining and instructive.

I need hardly add that no tricks, such as marking or tilting the vessels, are allowed.

1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Measuring, Weighing, and Packing Puzzles: $183$. -- At the Brook
1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Combinatorial & Topological Problems: Liquid Pouring Puzzles: $403$. At the Brook