Part 26
Friends Sir, friends, stand your disposition; I bearing a man the world is whilst the contempt, ridicule. are ambitious.
44. A PUZZLING INSCRIPTION.
P R S V R Y P R F C T M N V R K P T H S P R C P T S T N.
The two lines above were affixed to the communion table of a small church in Wales, and continued to puzzle the learned congregation for several centuries, but at length the inscription was deciphered. What was it?
45. THE PUZZLING RINGS.
This perplexing invention is of great antiquity, and was treated on by Cardan, the mathematician, at the beginning of the sixteenth century. It consists of a flat piece of thin metal or bone, with ten holes in it; in each hole a wire is loosely fixed, beaten out into a head at one end, to prevent its slipping through, and the other fastened to a ring, also loose. Each wire has been passed through the ring of the next wire, previously to its own ring being fastened on; and through the whole of the rings runs a wire loop or bow, which also contains, within its oblong space, all the wires to which the rings are fastened; the whole presenting so complicated an appearance, as to make the releasing the rings from the bow appear an impossibility. The construction of it would be found rather troublesome to the amateur, but it may be purchased at most of the toy shops very lightly and elegantly made. It also exists in various parts of the country, forged in iron, perhaps by some ingenious village mechanic, and aptly named "The Tiring Irons." The following instructions will show the principle on which the puzzle is constructed, and will prove a key to its solution.
Take the loop in your left hand, holding it at the end, B, and consider the rings as being numbered 1st to 10th. The 1st will be the extreme ring to the right, and the 10th the nearest your left hand.
It will be seen that the difficulty arises from each ring passing round the wire of its right-hand neighbor. The extreme ring at the right hand, of course, being unconnected with any other wire than its own, may at any time be drawn off the end of the bow at A, raised up, dropped through the bow, and finally released. After you have done this, try to pass the second ring in the same way, and you will not succeed, as it is obstructed by the wire of the first ring; but if you bring the first ring on again, by reversing the process by which you took it off, viz., by putting it up through the bow, and on to the end of it, you will then find that by taking the first and second rings together, they will both draw off, lift up, and drop through the bow. Having done this, try to pass the third ring off, and you will not be able; because it is fastened on one side to its own wire, which is within the bow, and on the other side to the second ring, which is without the bow. Therefore, leaving the third ring for the present, try the fourth ring, which is now at the end all but one, and both of the wires which affect it being within the bow, you will draw it off without obstruction; and, in doing this, you will have to slip the third ring off, which will not drop through for the reasons before given; so, having dropped the fourth ring through, you can only slip the third ring on again. You will now comprehend that (with the exception of the first ring) the only ring which can at any time be released is that which happens to be second on the bow, at the right-hand end; because both the wires which affect it being within the bow, there will be no impediment to its dropping through. You have now the first and second rings released, and the fourth also--the third still fixed; to release which we must make it last but one on the bow, and to effect which pass the first and second rings together through the bow, and on to it; then release the first ring again by slipping it off and dropping it through, and the third ring will stand as second on the bow, in its proper position for releasing, by drawing the second and third off together, dropping the third through, and slipping the second on again. Now to release the second, put the first up, through and on the bow; then slip the two together off, raise them up, and drop them through. The sixth will now stand second, consequently in its proper place for releasing; therefore draw it toward the end, A, slip the fifth off, then the sixth, and drop it through; after which replace the fifth, as you cannot release it until it stands in the position of a second ring; in order to effect this you must bring the first and second rings together, through and on to the bow; then in order to get the third on, slip the first off and down through the bow; then bring the third up, through and on to the bow; then bring the first ring up and on again, and, releasing the first and second together, bring the fourth through and on to the bow, replacing the third; then bring the first and second together on, drop the first off and through, then the third the same, replace the first on the bow, take off the first and second together, and the fifth will then stand second, as you desired; draw it toward the end, slip it off and through, replace the fourth, bring the first and second together up and on again, release the first, bring on the third, passing the second ring on to the bow again, replace the first, in order to release the first and second together; then bring the fourth toward the end, slipping it off and through, replace the third, bring the first and second together up and on again, release the first, then the third, replacing the second, bring the first up and on, in order to release the first and second together, which having done, your eighth ring will then stand second, consequently you can release it, slipping the seventh on again. Then to release the seventh, you must begin by putting the first and second up and on together, and going through the movements in the same succession as before, until you find you have only the tenth and ninth on the bow; then slip the tenth off and through the bow, and replace the ninth. This dropping of the tenth ring is the first effectual movement toward getting the rings off, as all the changes you have gone through were only to enable you to get at the tenth ring. You will then find that you have only the ninth left on the bow, and you must not be discouraged on learning, that in order to get that ring off, all the others to the right hand must be put on again, beginning by putting the first and second together, and working as before, until you find that the ninth stands as second on the bow, at which time you can release it. You will then have only the eighth left on the bow; you must again put on all the rings to the right hand, beginning by putting up the first and second together, till you find the eighth standing as second on the bow, or in its proper position for releasing; and so you proceed until you find all the rings finally released. As you commence your operations with all the rings ready fixed on the bow, you will release the tenth ring in one hundred and seventy moves; but as you then have only the ninth on, and as it is necessary to bring on again all the rings up to the ninth, in order to release the ninth, and which requires fifteen moves more, you will, consequently, release the ninth ring in two hundred and fifty-six moves; and, for your encouragement, your labor will diminish, by one half, with each following ring which is finally released. The eighth comes off in one hundred and twenty-eight moves, the seventh in sixty-four moves, and so on, until you arrive at the second and first rings, which come off together, making six hundred and eighty-one moves, which are necessary to take off all the rings. With the experience you will by this time have acquired, it is only necessary to say, that to replace the rings, you begin by putting up the first and second together, and follow precisely the same system as before.
46. MOVING THE KNIGHT OVER ALL THE SQUARES ALTERNATELY.
The problem respecting the placing the knight on any given square, and moving him from that square to any house on the board, has not been thought unworthy the attention of the first mathematicians. Euler, Ozanam, De Montmart, De Moivre, De Majron, and others, have all given methods by which this feat might be accomplished. It was reserved, however, for the present century to lay this down on a general plan; and the only English writer who has noticed this is Mr. George Walker, in his _Treatise on Chess_. The plan is this: Let the knight be placed on any square, and move him from square to square, on the principle of always playing him to that point, from which, in actual play, he would command the fewest other squares; observing, that in reckoning the squares commanded by him you must omit such as he has already covered. If, too, there are two squares, on both of which his powers would be equal, you may move him to either. Try this on the board, with some counters or wafers, placing one on every square; and, when you clearly understand it, you may astonish your friends by inviting them to station the knight on any square they like, and engaging to play him, from that square, over the remaining sixty-three in sixty-three moves. When the automaton Chessplayer was last exhibited in England, this was made part of the wonders he accomplished, though as the above plan was not then known here, he could not adopt it, but used something like the method laid down by Euler, and which we subjoin.
Our young Chess-players must remember that it does not matter on which square the knight is placed at starting; as, by acquiring the plan by heart, which is soon done, he can play him over all the squares from any given point, his last square being at the distance of a knight's move from his first. It is obvious that this route may be varied many ways, and we have often amused ourselves by trying to work it on a slate.
ANOTHER METHOD.
The problem of the knight's covering successively each square of the board, has, in all ages, attracted the attention of the first mathematicians; it is only lately, however, that this very ingenious system for performing the feat without seeing the board, has been invented by an Edinburgh gentleman. We well recollect the surprise occasioned among chess-amateurs when it was first performed; indeed it was generally considered a greater mental effort than that of playing three games of chess at the same time, without seeing the board.
The general rule for moving the Knight upon all the squares of the board, is to commence by moving him to that square which commands the fewest points of attack, and by continuing this principle he will occupy all the squares in rotation, observing, that if on any two or more squares his power would be equal, he may be placed indifferently on either of such squares. Thus we see, that there are different routes which the Knight-errant may take in his progress over all the board; still, whichever of these routes for covering the sixty-four squares may be adapted, each move forms, if we may so express ourselves, a link in an endless chain, so that whatever square we start from, by taking one known route, we are sure to arrive at a square, the last link of the chain, a Knight's move distant from the square of our departure. Consequently, if any person could commit to memory the consecutive moves of any one route over the board, he would be able to start from any one square in that route, in the same manner that any of us, if required to mention the numerals up to sixty-four, could as easily start at thirty and end at twenty-nine, as if we started at one and ended at sixty-four.
+------+------+------+------+------+------+------+------+ | | | | | | | | | | Met. | Let. | Ket. | Het. | Get. | Fet. | Det. | Bet. | +------+------+------+------+------+------+------+------+ | | | | | | | | | | Men. | Len. | Ken. | Hen. | Gen. | Fen. | Den. | Ben. | +------+------+------+------+------+------+------+------+ | | | | | | | | | | Mix. | Lix. | Kix. | Hix. | Gix. | Fix. | Dix. | Bix. | +------+------+------+------+------+------+------+------+ | | | | | | | | | | Miv. | Liv. | Kiv. | Hiv. | Giv. | Fiv. | Div. | Biv. | +------+------+------+------+------+------+------+------+ | | | | | | | | | | Mor. | Lor. | Kor. | Hor. | Gor. | For. | Dor. | Bor. | +------+------+------+------+------+------+------+------+ | | | | | | | | | | Mee. | Lee. | Kee. | Hee. | Gee. | Fee. | Dee. | Bee. | +------+------+------+------+------+------+------+------+ | | | | | | | | | | Moo. | Loo. | Koo. | Hoo. | Goo. | Foo. | Doo. | Boo. | +------+------+------+------+------+------+------+------+ | | | | | | | | | | Mun. | Lun. | Kun. | Hun. | Gun. | Fun. | Dan. | Bun. | +------+------+------+------+------+------+------+------+ M L K H G F D B
These considerations greatly reduce the apparent impossibility of performing the feat; but the reader will exclaim, "What an immense undertaking it would be, to commit to memory the moves forming a Knight's route over the sixty-four squares!" and we reply, "Certainly it would be, if we used the language of Chess to designate the squares;" and herein lies the beauty of the invention. A set of names, whose application can be understood at a glance, are invented for the squares, and the performer of the feat, having learned a route of the Knight, expressed by these invented names, thinks in the new language which he directs the moves in the terms of chess--just as many of us _think_ in English, when we are writing or speaking French.
The diagram given above represents the chess-board; the distinction of white and black squares is not necessary for our purpose. The files, commencing from the right hand are distinguished by the consonants in alphabetical succession (C and J are, for obvious reasons, omitted.) Thus, the King's rook's file is known as B, the King's Knight's as D, the King's Bishops as F, the King's as G, the Queen's as H, the Queen's Bishop's as K, the Queen's Knight's as L, and the Queen's Rook's as M. This is all that has to be learned, in this system of Chess notation; for the lines of squares tell their own numbers--one being _un_, two _oo_, three _ee_, four _or_, six _ix_, seven _en_, eight _et_--being, in fact, the terminal sounds of the first eight numerals. Bun being B _one_, or King's Rook's square; Gix, G _six_, or King's sixth square. We consider it quite unnecessary to say another word in explanation of this system; its ingenious simplicity causes it to be understood and learned at a glance. All that is required now is, to select a Knight's route over all the squares of the board, and commit it to memory, not in the complicated terms of Chess, but in these simple equivalents. Suppose we start from the Queen's Knights seventh square, _len_, the route will be as follows:
Len het fen bet. Dix bor doo gun Koo mun lee kun. Moo kee goo dun. Bee div ben fet. Hen let mix lor. Hee kiv gor hix. Liv men ket gen. Kix giv fee hor. Gix for hiv gee. Fiv den biv dee. Bun foo hun loo. Mor lix met ken. Get fix det bix. Dor boo fun hoo. Lun mee kor miv
The only trouble is to commit this cabalistical-looking table to memory, which may be all accomplished in half an hour; the process will be greatly facilitated by the learner frequently playing the route over on the chess-board. He will be amply rewarded by the astonishment he will cause to the _natives_ of his locality, who may have the great misfortune of being unacquainted with our book's enlightening pages; and, if not quite a first-rate player, he will acquire an intimate knowledge of the peculiar powers and perplexing peregrinations of the eccentric _Caballeros_, who
"----fiery coursers guide With headlong speed throng wars empurpled tide; Alert and brave they spring amidst the fight, From white to black, from black to candid white."
ANOTHER METHOD.
Let Black Queen's Rook's Square count 1, (as in the diagram,) Black King's Rook 8, and count all the other Squares in the same way from 9 to 64. Place the Knight upon Black King's Rook's Square, 8, and move as follows: 23, 40, 55, 61, 51, 57, 42, 25, 10, 4, 14, 24, 39, 56, 62, 52, 58, 41, 26, 9, 3, 13, 7, 22, 32, 47, 64, 54, 60, 50, 33, 18, 1, 11, 5, 15, 21, 6, 16, 31, 48, 63, 53, 59, 49, 34, 17, 2, 12, 27, 44, 38, 28, 43, 37, 20, 35, 45, 30, 36, 18, 29, and 46. It may be well to chalk the figures on the board, as a guide, until the feat is well understood.
47. ROSAMOND'S BOWER.
The subjoined cut represents, it is said, the Maze at Woodstock, in which King Henry placed Fair Rosamond to protect her from the Queen. It certainly is a most ingenious contrivance, and may be made productive of much amusement. The puzzle consists in getting, from one of the numerous outlets, to the bower in the center, without crossing any of the lines.
ROSAMOND'S BOWER.
48. A MAZE OR LABYRINTH.
This maze is a correct ground-plan of one in the gardens of the Palace of Hampton Court. No legendary tale is attached to it, of which we are aware, but its labyrinthine walks occasion much amusement to the numerous holiday parties who frequent the palace grounds. The puzzle is to get into the center, where seats are placed under two lofty trees; and many are the disappointments experienced before the end is attained; and even then, the trouble is not over, it being quite as difficult to get _out_ as to get _in_.
49. THE CHINESE PUZZLE.
This puzzle, being one for the purpose of constructing different figures by arranging variously-shaped pieces of card or wood in certain ways, requires no separate explanation. Cut out of very stiff cardboard, or thin mahogany, which is decidedly preferable, seven pieces, in shape like the annexed figures and bearing the same proportion to each other; one piece must be made in the shape of figure 1, one of figure 2, and one of figure 3, and two of each of the other figures. The combinations of which these figures are susceptible, are almost infinite; and we subjoin a representation of a few of the most curious. It is to be borne in mind, that all the pieces of which the puzzle consists, must be employed to form each figure.
50. TROUBLE-WIT.
Take a sheet of stiff paper, fold it down the middle of the sheet, longways; then turn down the edge of each fold outward, the breadth of a penny; measure it as it is folded, into three equal parts, with compasses, which make six divisions in the sheet; let each third part be turned outward, and the other, of course, will fall right; then pinch it a quarter of an inch deep, in plaits, like a ruff, so that, when the paper lies pinched in its form, it is in the fashion represented by A; when closed together, it will be like B; unclose it again, shuffle it with each hand, and it will resemble the shuffling of a pack of cards; close it and turn each corner inward with your fore finger and thumb, it will appear as a rosette for a lady's shoe, as C; stretch it forth, and it will resemble a cover for an Italian couch, as D; let go your fore finger at the lower end, and it will resemble a wicket, as E; close it again, and pinch it at the bottom, spreading the top, and it will represent a fan, as F; pinch it half way, and open the top, and it will appear in the form shown by G; hold it in that form, and with the thumb of your left hand turn out the next fold, and it will be as H.
In fact, by a little ingenuity and practice, Trouble-wit may be made to assume an infinite variety of forms, and be productive of very considerable amusement.
ANSWERS TO PRACTICAL PUZZLES.
1. THE CHINESE CROSS ANSWER.
Place Nos. 1 and 2 close together, as in Fig. 1; then hold them together with the finger and thumb of the left hand horizontally and with the square hole to the right. Push No. 3--placed in the same position _facing you_ (_a_) in No. 4--through the opening at K, and slide it to the left at A, so that the profile of the pieces should be as in Fig. 2. Now push No. 4 _partially_ through the space from below upwards, as seen in f, Fig. 2. Place No. 5 cross-ways upon the part Y, so that the point R is directed upwards to the right hand side; then push No. 4 quite through, and it will be in the position shown by the dotted lines in Fig. 2. All that now remains is to push No. 6--which is the key--through the opening M and the cross is completed as in Fig. 3.
2. ANSWER TO THE "PARALLELOGRAM."
Divide the piece of card into five steps, and by shifting the position of the pieces, the desired figures may be obtained.
3. THE DIVIDED GARDEN ANSWER.
4. ANSWER TO THE ENDLESS STRING.
The string must be put through the armhole, and over the head, then through the opposite armhole; then the hand must be put up underneath the waistcoat, and the string drawn down around the body until the former drops down about the waist, when the experimenter may jump out of it and claim his coat.
5. ANSWER TO THE CHINESE MAZE.
KOONG-SEE'S WHISPERS.
A Why linger near the fence? a word or two Would kindle up a flame for ever true. B Beware of rivals--mischief hovers near; Or, worse mischance, parental frowns appear. C Favored indeed, the open door to gain-- Let no dishonor now your conduct stain. E The ground is rough, and difficult the road; But, faint not, thou shalt reach thy love's abode! F Against thy course runs the opposing tide, And waves of trouble cast thy hopes aside. G A modest competence thy lot will be; But richer joys than wealth are stored for thee. A Take heed! take heed! a strange transforming doom May fix thy love, but never let it bloom. J Be not too rash--nor leap the Bridge of Love, Leaving fond eyelids, moist with tears, above. K What dost thou on the house top? do not steal Thy love, but win by dutiful appeal! L A barren path this way thy footsteps tread; Thy heart will soon grow cold, thy love be fled. M Thou hast a friend can help thy onward way-- And such a friend will ne'er thy trust betray. D Joy! thou hast reached, at length, the wedding ring; Let white-robed maidens orange blossoms bring; Oh may your years of happy wedlock be Bright as your hopes, and from misgiving free.
6. ANSWER TO VERTICAL LINE PUZZLE.
7. THE THREE RABBITS, ANSWER.
8. THE ACCOMMODATING SQUARE.
9. ANSWER TO THE CIRCLE PUZZLE.
Thrust it upwards from the other side.
10. ANSWER TO THE CUT CARD PUZZLE.
Double the cardboard or leather lengthways down the middle, and then cut first to the right, nearly to the end, (the narrow way,) and then to the left, and so on to the end of the card; then open it and cut down the middle, except the two ends. The diagram shows the proper cuttings. By opening the card or leather, a person may pass through it. A laurel leaf may be treated in the same manner.
11. ANSWER TO THE BUTTON PUZZLE.