Henry Ernest Dudeney/Puzzles and Curious Problems/Magic Square, Measuring, Weighing, and Packing Problems

Henry Ernest Dudeney: Puzzles and Curious Problems: Magic Square, Measuring, Weighing, and Packing Problems

$289$ - Magic Square Trick

Place in the empty squares such figures (different in every case, and no two squares containing the same figure)

so that they shall add up to $15$ in as many straight directions as possible.

$\qquad \begin{array} {|c|c|c|} \hline \ \ & \ \ & \ \ \\ \hline \ \ & 5 & \ \ \\ \hline \ \ & \ \ & \ \ \\ \hline \end{array}$

$290$ - A Four-Figure Magic Square

In this square, as every cell contains the same number -- $1234$ -- the three columns, three rows and two long diagonals naturally add up alike.

$\qquad \begin{array} {|c|c|c|} \hline 1234 & 1234 & 1234 \\ \hline 1234 & 1234 & 1234 \\ \hline 1234 & 1234 & 1234 \\ \hline \end{array}$

The puzzle is to form and place nine different $4$-figure numbers (using the same figures) so that they shall form a perfect magic square.

That is, the numbers all together must contain nine of each of $1$, $2$, $3$ and $4$, and they must be proper numbers without using fractions or any other trick like that.

$291$ - Progressive Squares

This is a magic square, adding up to $287$ in every row, every column, and each of the two diagonals.

If we remove the outer margin of numbers we have another square giving sums of $205$.

If we again remove the margin there is left a magic square adding up to $123$.

Now fill up the vacant spaces in the diagram with such numbers from $1$ to $81$ inclusive as have not already been given,

so that there shall be formed a magic square adding up to $369$ in each of twenty directions.

$292$ - Conditional Magic Square

Can you form a magic square with all the columns rows, and two long diagonals, adding up alike,

with numbers $1$ to $25$ inclusive, placing only the odd numbers on the shaded squares in the diagram,

and the even numbers on the other squares?

$293$ - The Twenty Pennies

If sixteen pennies are arranged in the form of a square

there will be the same number of pennies in every row, column and each of the long diagonals.

Can you do the same with twenty pennies?

$294$ - The Keg of Wine

A man had a $10$-gallon keg of wine and a jug.

One day he drew off a jugful of wine and filled up the keg with water.

Later on, when the wine and water had got thoroughly mixed, he drew off another jugful, and again filled up the keg with water.

The keg then contained equal quantities of wine and water.

What was the capacity of the jug?

$295$ - Blending the Teas

A grocer buys two kinds of tea --

one at $2 \shillings 8 \oldpence$ per pound,

and the other, a better quality, at $3 \shillings 4 \oldpence$ per pound.

He mixes together some of each, which he proposes to sell at $3 \shillings 7 \oldpence$ a pound,

and so make a profit of $25$ per cent on the cost.

How many pounds of each kind must he use to make a mixture of $100$ pounds weight?

$296$ - Water Measurement

A maid was sent to the brook with two vessels that exactly measured $7$ pints and $11$ pints exactly.

She had to bring back exactly $2$ pints of water.

What is the smallest possible number of transactions necessary?

$297$ - Mixing the Wine

A glass is one-third full of wine,

and another glass, with equal capacity, is one-fourth full of wine.

Each is filled with water and their contents mixed in a jug.

Half of the mixture is poured into one of the glasses.

What proportion of this is wine and what part water?

$298$ - The Stolen Balsam

Three men robbed a gentleman of a vase containing $24$ ounces of balsam.

While running away, they met in the forest a glass seller, of whom, in a great hurry, they purchased three vessels.

On reaching a place of safety they wished to divide the booty,

but they found that their vessels contained $5$, $11$, and $13$ ounces respectively.

How could they divide the balsam into equal portions?

$299$ - The Weight of the Fish

A man caught a fish.

The tail weighed $9$ ounces.

The head weighed as much as the tail and half the body,

and the body weighed as much as the head and tail together.

What is the weight of the fish?

$300$ - Fresh Fruits

Some fresh fruit was being weighed for some domestic purpose.

It was found that the apples, pears and plums exactly balanced each other as follows:

One pear and three apples weigh the same as $10$ plums;

and one apple and six plums weigh the same as one pear.

How many plums alone would weigh the same as one pear?

$301$ - Weighing the Tea

A grocer proposed to put up $20$ pounds of China tea into $2$-pound packets,

but the weights had been misplaced by somebody, and he could only find the $5$-pound and the $9$-pound weights.

What is the quickest way for him to do the business?

We will say at once that only nine weighings are really necessary.

$302$ - Delivering the Milk

A milkman one morning was driving to his dairy with two $10$-gallon cans full of milk,

when he was stopped by two countrywomen, who implored him to sell them a quart of milk each.

Mrs. Green had a jug holding exactly $5$ pints, and Mrs. Brown a jug holding exactly $4$ pints,

but the milkman had no measure whatsoever.

How did he manage to put an exact quart into each of the jugs?

It was the second quart that gave all the difficulty.

But he contrived to do it in as few as nine transactions --

and by a "transaction" we mean the pouring from a can into a jug, or from one jug to another, or from a jug back to the can.

How did he do it?