Henry Ernest Dudeney/Modern Puzzles/Measuring, Weighing, and Packing Problems

Henry Ernest Dudeney: Modern Puzzles: Measuring, Weighing, and Packing Problems

$180$ - The Damaged Measure

A young man has a yardstick from which $3$ inches have been broken off,

so that it is only $33$ inches in length.

Some of the graduation marks are also obliterated, so that only eight of these marks are legible;

yet he is able to measure any given number of inches from $1$ inch up to $33$ inches.

Where are these marks placed?

$181$ - The Six Cottages

A circular road, $27$ miles long, surrounds a tract of wild and desolate country,

and on this road are $6$ cottages so placed that one cottage or another is at a distance of one, two, three up to $26$ miles inclusive from some other cottage.

Thus, Brown may be a mile from Stiggins, Jones two miles from Rogers, Wilson three miles from Jones, and so on.

Of course, they can walk in either direction if required.

Can you place the cottages at distances that will fulfil the conditions?

The illustration is intended to give no clue as to the relative distances.

$182$ - A New Domino Puzzle

Two dominoes have been placed together so that by taking the pips in unbroken conjunction

I can get all the numbers from $1$ to $9$ inclusive.

Thus, $1$, $2$ and $3$ can be taken alone;

then $1$ and $3$ make $4$; $3$ and $2$ make $5$; $3$ and $3$ make $6$;

$1$, $3$ and $3$ make $7$; $3$, $3$ and $2$ make $8$, and $1$, $3$, $3$ and $2$ make $9$.

It would not have been allowed to take the $1$ and the $2$ to make $3$, nor to take the first $3$ and the $2$ to make $5$.

The numbers would not have been in conjunction.

Now try to arrange four dominoes so that you can make the pips in this way sum to any number from $1$ to $24$ inclusive.

The dominoes need not be placed $1$ against $1$, $2$ against $2$, and so on, as in play.

$183$ - At the Brook

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.

$184$ - A Prohibition Poser

The American Prohibition authorities discovered a full barrel of beer,

and were about to destroy the liquor by letting it run down a drain

when the owner pointed to two vessels standing by and begged to be allowed to retain in them a small quantity for the immediate consumption of his household.

One vessel was a $7$-quart and the other a $5$-quart measure.

The officer was a wag, and, believing it to be impossible, said that if the man could measure an exact quart into each vessel

(without any pouring back into the barrel) he might do so.

How was it to be done in the fewest possible transactions without any marking or other tricks?

Pouring down the drain counts as one transaction.

Perhaps I should state that an American barrel of beer contains exactly $120$ quarts.

$185$ - Prohibition Again

Let us now try to discover the fewest possible manipulations under the same conditions as in the last puzzle,

except that we may now pour back into the barrel.

$186$ - The False Scales

A pudding, when placed into one of the pans of a balance, appeared to weigh $4$ ounces more than $\tfrac 9 {11}$ of its true weight,

but when placed into the other pan it appeared to weigh $3$ pounds more than in the first pan.

What was its true weight?

$187$ - Weighing the Goods

A tradesman whose morals had become corrupted during the war by a course of profiteering went to the length of introducing a pair of false scales.

It will be seen from the diagram that one arm is longer than the other,

though they are purposely drawn so as to give no clue as to the answer.

As a consequence, it happened that in one of the cases exhibited eight of the little packets

(it does not matter what they contain)

exactly balanced three of the canisters,

while in the other case one packet appeared to be of the same weight as $6$ canisters.

Now, as the true weight of one canister was known to be exactly one ounce, what was the true weight of the eight packets?

$188$ - Monkey and Pulley

A rope is passed over a pulley.

It has a weight at one end and a monkey at the other.

There is the same length of rope on either side and equilibrium is maintained.

The rope weighs four ounces per foot.

The age of the monkey and the age of the monkey's mother total four years.

The weight of the monkey is as many pounds as the monkey's mother is years old.

The monkey's mother is twice as old as the monkey was

when the monkey's mother was half as old as the monkey will be

when the monkey is three times as old as the monkey's mother was

when the monkey's mother was three times as old as the monkey.

The weight of the rope and the weight at the end was half as much again as the difference in weight

between the weight of the weight and the weight and the weight of the monkey.

Now, what was the length of the rope?

$189$ - Weighing the Baby

There was a family group at the automatic weighing machine, trying to weigh the baby.

Whenever they put the baby on the machine, she always yelled and rolled off,

while the father was holding off the dog, who always insisted on being included in the operations.

At last the man, with the baby and Fido, were on the machine together.

The dial read $180$ pounds.

The man turned to his wife and said,

"Baby and I weigh $162$ pounds more than the dog,

while the dog weighs $70$ per cent less than the baby.

We must try to work it out at home."

What was the actual weight of the baby?

$190$ - Packing Cigarettes

A manufacturer sends out his cigarettes in boxes of $160$;

they are packed in $8$ rows of $20$ each, and exactly fill the box.

Could he, by packing differently, get more cigarettes than $160$ into the box?

If so, what is the greatest number that he could add?