Henry Ernest Dudeney/Modern Puzzles/Measuring, Weighing, and Packing Problems
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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;
- Where are these marks placed?
$181$ - The Six Cottages
- A circular road, $27$ miles long, surrounds a tract of wild and desolate country,
- 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,
- 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
- The weight of the rope and the weight at the end was half as much again as the difference in weight
- 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,
- 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?