53. HEARD ON THE TUBE RAILWAY. First Lady: "And was he related to you, dear?"

Second Lady: "Oh, yes. You see, that gentleman's mother was my mother's mother-in-law, but he is not on speaking terms with my papa."

First Lady: "Oh, indeed!" (But you could see that she was not much wiser.)

How was the gentleman related to the Second Lady?

SOLUTION TO 217. THE TWICKENHAM PUZZLE. 

Play the counters in the following order: K C E K W T C E H M K W T A N C E H M I K C E H M T, and there you are, at Twickenham. The position itself will always determine whether you are to make a leap or a simple move.

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55. A MIXED PEDIGREE. Joseph Bloggs: "I can't follow it, my dear boy. It makes me dizzy!"

John Snoggs: "It's very simple. Listen again! You happen to be my father's brother-in-law, my brother's father-in-law, and also my father-in-law's brother. You see, my father was--"

But Mr. Bloggs refused to hear any more. Can the reader show how this extraordinary triple relationship might have come about?

SOLUTION TO 330. THE YACHT RACE. 

The diagram explains itself. The numbers will show the direction of the lines in their proper order, and it will be seen that the seventh course ends at the flag-buoy, as stipulated.

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This puzzle will call for a lot of skilful seamanship on account of the sharp angles at which it will occasionally be necessary to tack. The point of a lead pencil and a good nautical eye are all the outfit that we require.

This is difficult, because of the condition as to the flag-buoy, and because it is a re-entrant tour. But again we are allowed those oblique lines. (2/2)

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330. THE YACHT RACE. Now then, ye land-lubbers, hoist your baby-jib-topsails, break out your spinnakers, ease off your balloon sheets, and get your head-sails set!

Our race consists in starting from the point at which the yacht is lying in the illustration and touching every one of the sixty-four buoys in fourteen straight courses, returning in the final tack to the buoy from which we start. The seventh course must finish at the buoy from which a flag is flying.
(1/2)

SOLUTION TO 168. THE CHRISTMAS PUDDING. (2/2) 

...
to the opposite edge. And similar variations may be introduced at other places.

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SOLUTION TO 168. THE CHRISTMAS PUDDING. (1/2) 

The illustration shows how the pudding may be cut into two parts of exactly the same size and shape. The lines must necessarily pass through the points A, B, C, D, and E. But, subject to this condition, they may be varied in an infinite number of ways. For example, at a point midway between A and the edge, the line may be completed in an unlimited number of ways (straight or crooked), provided it be exactly reflected from E

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SOLUTION TO 315. THE HAT-PEG PUZZLE. (2/2) 

...
square farther to the left. This is, I believe, the only solution to the puzzle.

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SOLUTION TO 315. THE HAT-PEG PUZZLE. (1/2) 

The moves will be made quite clear by a reference to the diagrams, which show the position on the board after each of the four moves. The darts indicate the successive removals that have been made. It will be seen that at every stage all the squares are either attacked or occupied, and that after the fourth move no queen attacks any other. In the case of the last move the queen in the top row might also have been moved one

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and finally a fourth queen. After the fourth move every square must be attacked or occupied, but no queen must then attack another. Of course,
the moves need not be "queen moves;" you can move a queen to any part of the board. (2/2)

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315. THE HAT-PEG PUZZLE. Here is a five-queen puzzle that I gave in a fanciful dress in 1897. As the queens were there represented as hats on sixty-four pegs, I will keep to the title, "The Hat-Peg Puzzle." It will be seen that every square is occupied or attacked. The puzzle is to remove one queen to a different square so that still every square is occupied or attacked,
then move a second queen under a similar condition, then a third queen, (1/2)

SOLUTION TO 268. THE PEAL OF BELLS. (2/2) 

...
solution is possible for any number of bells under the conditions previously stated.

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SOLUTION TO 268. THE PEAL OF BELLS. (1/2) 

The bells should be rung as follows:--

1 2 3 4
2 1 4 3
2 4 1 3
4 2 3 1
4 3 2 1
3 4 1 2
3 1 4 2
1 3 2 4
3 1 2 4
1 3 4 2
1 4 3 2
4 1 2 3
4 2 1 3
2 4 3 1
2 3 4 1
3 2 1 4
2 3 1 4
3 2 4 1
3 4 2 1
4 3 1 2
4 1 3 2
1 4 2 3
1 2 4 3
2 1 3 4

I have constructed peals for five and six bells respectively, and a

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last change must be able to pass into the first. These fantastic conditions will be found to be observed in the little peal for three bells, as follows:--

1 2 3
2 1 3
2 3 1
3 2 1
3 1 2
1 3 2

How are we to give him a correct solution for his four bells? (2/2)

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268. THE PEAL OF BELLS. A correspondent, who is apparently much interested in campanology, asks me how he is to construct what he calls a "true and correct" peal for four bells. He says that every possible permutation of the four bells must be rung once, and once only. He adds that no bell must move more than one place at a time, that no bell must make more than two successive strokes in either the first or the last place, and that the (1/2)

SOLUTION TO 185. ST. GEORGE'S BANNER. 

As the flag measures 4 ft. by 3 ft., the length of the diagonal (from corner to corner) is 5 ft. All you need do is to deduct half the length of this diagonal (2½ ft.) from a quarter of the distance all round the edge of the flag (3½ ft.)--a quarter of 14 ft. The difference (1 ft.) is the required width of the arm of the red cross. The area of the cross will then be the same as that of the white ground.

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In the centre of the estate was a well, indicated by the dark spot, and Benjamin, Charles, and David complained that the division was not
"equitable," since Alfred had access to this well, while they could not reach it without trespassing on somebody else's land. The puzzle is to show how the estate is to be apportioned so that each son shall have land of the same shape and area, and each have access to the well without going off his own land. (2/2)

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180. THE FOUR SONS. Readers will recognize the diagram as a familiar friend of their youth. A man possessed a square-shaped estate. He bequeathed to his widow the quarter of it that is shaded off. The remainder was to be divided equitably amongst his four sons, so that each should receive land of exactly the same area and exactly similar in shape. We are shown how this was done. But the remainder of the story is not so generally known. (1/2)

SOLUTION TO 21. A DEAL IN APPLES. 

I was first offered sixteen apples for my shilling, which would be at the rate of ninepence a dozen. The two extra apples gave me eighteen for a shilling, which is at the rate of eightpence a dozen, or one penny a dozen less than the first price asked.

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