Henry Ernest Dudeney/Puzzles and Curious Problems/Crossing River Problem, and Problems Concerning Games and Puzzle Games

Henry Ernest Dudeney: Puzzles and Curious Problems: Crossing River Problem, and Problems Concerning Games and Puzzle Games

$303$ - Crossing the River

During the Turkish stampede in Thrace, a small detachment found itself confronted by a wide and deep river.

However, they discovered a boat in which two children were rowing about.

It was so small that it would only carry the two children, or one grown up person.

How did the officer get himself and his $357$ soldiers across the river and leave the two children finally in joint possession of their boat?

And how many times need the boat pass from shore to shore?

$304$ - Grasshoppers' Quadrille

It is required to make the white men change places with the black men in the fewest possible moves.

There is no diagonal play, nor are there captures.

The white men can only move to the right or downwards, and the black men to the left or upwards,

but they may leap over one of the opposite colour, as in draughts.

$305$ - Domino Frames

Take an ordinary set of $28$ dominoes and return double $3$, double $4$, double $5$, and double $6$ to the box as not wanted.

Now, with the remainder form three square frames, in the manner shown, so that the pips in every side shall add up alike.

In the example given the sides sum to $15$.

If this were to stand, the sides of the other two frames must also sum to $15$.

But you can take any number you like, and it will be seen that it is not required to place $6$ against $6$, $5$ against $5$, and so on, as in play.

$306$ - A Puzzle in Billiards

Alfred Addlestone can give Benjamin Bounce $20$ points in $100$, and beat him;

Bounce can give Charlie Cruikshank $25$ points in $100$, and beat him.

Now, how many points can Addlestone give Cruikshank in order to beat him in a game of $200$ up?

Of course we assume that the players play constantly with the same relative skill.

$307$ - Scoring at Billiards

What is the highest score that you can make in two consecutive shots at billiards?

$308$ - Domino Hollow Squares

It is required with the $28$ dominoes to form $7$ hollow squares, like the example given,

so that the pips in the four sides of every square shall add up alike.

All these seven squares need not have the same sum, and, of course, the example given need not be one of your set.

$309$ - Domino Sequences

A boy who had a complete set of dominoes, up to double $9$, was trying to arrange them all in sequence, in the usual way --

$6$ against $6$, $3$ against $3$, blank against blank, and so on.

His father said to him, "You are attempting an impossibility, but if you let me pick out $4$ dominoes it can them be done.

And those I take shall contain the smallest total number of pips possible in the circumstances.

Now, which dominoes might the father have selected?

$310$ - Two Domino Squares

Arrange the $28$ dominoes as shown in the diagram to form two squares

so that the pips in every one of the eight sides shall add up alike.

The constant addition must of course be within limits to make the puzzle possible,

and it will be interesting to find those limits.

Of course, the dominoes need not be laid according to the rule, $6$ against $6$, blank against blank, and so on.

$311$ - Domino Multiplication

Four dominoes may be so placed as to form a simple multiplication sum if we regard the pips as figures.

The example here shown will make everything perfectly clear.

Now, the puzzle is, using all the $28$ dominoes to arrange them so as to form $7$ such little sums in multiplication.

No blank may be placed at the left end of the multiplicand or product.

$312$ - Domino Rectangle

Arrange the $28$ dominoes exactly as shown in the diagram, where the pips are omitted,

so that the pips in every one of the seven columns shall sum to $24$, and the pips in every one of the eight rows to $21$.

The dominoes need not be $6$ against $6$, $4$ against $4$, and so on.

$313$ - The Domino Column

Arrange the $28$ dominoes in a column so that the three sets of pips, taken anywhere,

shall add up alike on the left side and on the right.

Such a column has been started in the diagram.

This is merely an example, so you can start afresh if you like.

$314$ - Card Shuffling

The rudimentary method of shuffling a pack of cards is to take the pack face downwards in the left hand and then transfer them one by one to the right hand,

putting the second on top of the third, the third under, the fourth above, and so on until all are transferred.

If you do this with any even number of cards and keep on repeating the shuffle in the same way,

the cards will in due time return to their original order.

Try with $4$ cards, and you will find the order is restored in $3$ shuffles.

In fact, where the number of cards is $2$, $4$, $8$, $16$, $32$, $64$,

the number of shuffles to get them back to the original arrangement is $2$, $3$, $4$, $5$, $6$, $7$ respectively.

Now, how many shuffles are necessary in the case of $14$ cards?

$315$ - Arranging the Dominoes

The number of ways the set of $28$ dominoes may be arranged in a straight line, in accordance with the original rule of the game,

left to right and right to left, in any arrangement counting as different ways,

is $7 \, 959 \, 229 \, 931 \, 520$.

After discarding all dominoes bearing a $5$ or a $6$, how many ways may the remaining $15$ dominoes be so arranged in a line?

$316$ - Queer Golf

A certain links had nine holes, $300$, $250$, $200$, $325$, $275$, $350$, $225$, $375$, and $400$ yards apart.

If a man could always strike the ball in a perfectly straight line and send it exactly one of two distances,

so that it would either go towards the hole, pass over it, or drop into it,

what would those two distances be that would carry him in the least number of strokes round the whole course?

Two very good distances are $125$ and $75$, which carry you round in $28$ strokes,

but this is not the correct answer.

$317$ - The Archery Match

On a target on which the scoring was $40$ for the bull's-eye, and $39$, $24$, $23$, $17$ and $16$ respectively for the rings from the centre outwards, as shown in the diagram,

three players had a match with six arrows each.

The result was:

Miss Dora Talbot: $120$ points;

Reggie Watson, $110$ points;

Mrs. Finch, $100$ points.

Every arrow scored, and the bull's-eye was only once hit.

Can you, from these facts, determine the exact six hits made by each competitor?

$318$ - Target Practice

Three people in an archery competition had each had six shots at a target, and the result is shown in the diagram,

where they all hit the target every time.

The bull's-eye scores $50$, then the scores are $25$, $20$, $10$, $5$, $3$, $2$, $1$ for the rings from the centre outwards respectively.

It is seen that the hits on target are $1$ bull's-eye, two $25$s, three $20$s, three $10$s, three $1$s and two hits in each of the other rings.

The three men tied with an equal score.

Can you work out who hit what?

$319$ - The Ten Cards

Place any ten playing cards in a row face up.

There are two players.

The first player may turn face down any single card he chooses.

Then the second player can turn face down any single card or any $2$ adjacent cards.

And so on.

Thus the first player must turn face down a single, but afterwards either player may turn down either a single or two adjacent cards.

The player who turns down the last card wins.

Should the first or second player win?