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THE "15" AND 34" PUZZLES.

It is the simplest and best of the puzzles that familiarize boys with the behaviour of numbers in combinations and permutations.

The apparatus is simple enough, merely consisting of a box containing sixteen small wooden blocks, numbered from 1 to 16. That numbered 16 is withdrawn, and the rest arranged irregularly in the box. The puzzle consists in arranging them in this order-

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At first sight this seems easy enough, but a few minutes' practice will show the wonderful amount of complications which arise while shifting the pieces. The" 34" puzzle merely consists in arranging the sixteen blocks in the box in such a manner that they will add perpendicularly, horizontally, and diagonally; also in arranging the 4 in each corner, the four outside numbers of the two central rows, and the four groups in each corner, so that each will produce the same total-34.

THE STAFF PUZZLE.

This is formed of a staff made of box-wood, through the centre of which is a hole lengthways, and through this is passed a double cord; at the distance of 1 in. are knots, and at each end a button (Fig. 1). To free the staff from the buttons and cord is the puzzle.

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It is attainable thus (Fig. 2): The knot separated is a slip-knot-it is shown loose at Fig. 3. If the button is passed through the loop of the loosened knot it will free itself, and the other may be removed easily.

THE SIX-SQUARE PUZZLE.

Balls numbered from 1 to 12 are placed on a board to form the angles of six squares, as Fig. 1.

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To remove three balls so that the remaining nine are at the angles of three perfect squares is the puzzle. Fig. 2 will show how it is done.

THE VICTORIA PUZZLE.

This puzzle is constructed of two pieces of wood of the same shape, with a wooden button between, as Fig. I will show. Through these is passed a cord,

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uniting the three in such a manner that it forms a most puzzling puzzle to get them free from the cord. We are indebted to Mr. Cremer, of Regent Street, who is the inventor, for the following description, as well as for the permission to engrave the whole of the illustrations of Puzzles.

Take one of the end pieces in the left hand, pull the loop up through the centre and pass it through the hole nearest the round piece of wood, then draw the remaining two pieces through the loop, pull the loop back again through the hole, and the cord will readily come off.

In playing this, care must be taken that the cord does not get twisted.

THE ARTILLERY PUZZLE

is a box-wood cannon, with a small and large ball fixed by string at the breech internally. The puzzle is to remove these (Fig. 1). If the large ball is pulled, it will draw the smaller inside the cannon, and it cannot be extricated until the puzzle is played, which is done as follows:

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A tightly-fitting plug at the mouth of the cannon (Fig. 2), when removed, draws out the cord by means of a loop fixed to it, which will slip over the small ball, and then, by taking hold of the ball at the breech, they can be freed from the cannon with ease.

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Our apparatus will consist of the following: horizontal bar, hanging bar, parallel bars, vaulting-horse, ladder, hanging ropes, and the usual et ceteras. Of these latter, however, we shall not take notice here; our attention will be entirely directed to the more advanced exercises.

THE HORIZONTAL BAR should be set up as follows: If intended as a permanency, two strong posts must be let into the ground or into iron sockets, standing seven feet apart and about eight feet in height; these are to support the bar, which must be made to shift up and down in grooves cut in the posts, so as to be easily adapted to the height of the performer. This bar should be of straight-grained ash, seven feet between the uprights, an inch and threequarters in diameter, perfectly round, with a steel core an inch thick running through the centre. This latter is a very important point.

If there be no steel core, then the bar must be reduced at least one foot in length and increased to two inches diameter; both of which, especially the latter, as making it clumsy to the grasp of an ordinary hand, will detract much from its practical value.

The bar must be so fastened to the uprights that there shall be no unsteadiness or vibration. A wabbly bar is a terrible nuisance, and is apt to throw one out of all calculation just at the critical point of a feat.

If for private use, or it be thought desirable to make it portable, the method of construction figured in our cut (Fig. 1) will be found very convenient and serviceable, and, what is more, thoroughly trustworthy.

THE HANGING BAR must be very carefully constructed. The ropes should be attached securely to a good, firm, unyielding support, about fifteen or eighteen feet from the ground-this will be quite sufficient height—and the bar, which should be about twenty-six inches long by one-and-a-quarter in diameter, with a steel core as before, must be firmly attached to the ropes, so as to afford a safe hold. Above all things, it must not revolve in the grasp. The height from the ground must be regulated by the stature of the performer.

FIG. 2.

THE PARALLEL BARS are very seldom constructed with anything like correctness of shape or proportions. A couple of clumsy rails-one might almost say beams—laid across two pairs of posts at any height from the ground and at any distance apart, are set up, dubbed "parallel bars," and are supposed to be all that could be desired. But, as might be supposed if people only took the trouble to think, parallel bars, to be of any real service, require as nice an adaptation to their purposes as any other mechanical contrivance.

The bars or rails, being intended for the grasp of the hands, must be of such size and shape as will afford the best grasp, and their height and distance apart must be adapted to the stature of those for whose use they are intended. The size of the bars is especially important: if they be too large for a fair grasp, not only is the hand likely to slip and a heavy fall to result, but there is great danger to the wrist and thumb of serious sprains or dislocation. The

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