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SOME CHRISTMAS PUZZLES. Bx Hhnbx E. Dudeney. "There are nopuzzles in the crackers!" exclaimed the children over the Christmas dessert. This was • indeed a calamity. Fancy Ynletide without a single puzzle to try the wits of the young folk who happened to be so fond of these things! "They must have sent the wrong boxes," said Mrs Smiley. "I am so sorry,, children. What shall we do?" "Oh, if it's puinsles you want, I can give you plenty of them," Mr Binks declared, " for I ve been beset with posers and perplexities ever since I started lo leave home."

Simon Binks was an old bachelor friend of Mr Smiley, who had come a considerable distance to spend Christmas with the family. He was always a welcome fuest, especially to the children, for he ad a happy gift of providing entertainment in innumerable ways and of being equal to any occasion that might arise. The children clapped their hands in delight, for they had often tested Simon's quality. Of course, one cannot help suspecting that the puzzles he related had been prepared, and that, in fact, they really belonged to the domain of fiction; but such a question did not disturb tho young folk, who, like all sensible children, preferred to believe that tho fairy tales and other stories they heard were true in all essential details. CARRYING THE BAGS. "Well, children," said Mr Binks, " shall we start at the beginning or at the end? The beginning! Very well, then. When I set out from home my first perplexity began. The railway station is four miles from my house; I had two heavy bags of equal weight, and my horse had* suddenly gone lame. There was no time to hire a conveyance, so It was clear I must walk. But I could not alone manage the two bags. My gardener and the boy both insisted on carrying the luggage, but the gardener is an old man and the boy not sufficiently strong, and, as I believe in a fair division of labor, and in taking mv own share, I settled that we should all three walk to the station together and share the burden equally among us. So we started off with the gardener carrying one bag and the boy the other, while I worked out in my head the best way of arranging for the transfer of the bags as we wont along. How would you have done it? • While the company were working out this simple little poser Mr Binks remarked that they could each write down their answers on a sheet of paper and he would give, them the correct solutions at breakfast next day. THE STATION MASTER'S REPLY. "When we reached the railway station I asked the station master how long I had to wait for my train, and he answered: 'Too-too-too-too-too-too.' I overheard the boy say to the gardener; ' I should like to punch his head for speaking to _ the governor like that. Why can't he give a civil answer?' But the answer was quite civil when properly understood. Now, what did the station master mean by his curious trumpeting?" WHAT THE GUARD SAID. "At Wurzletown Junction an old lady put her head out of the window of my carriage and shouted: 'Guard! Guard! How long will the journey be from here to Mudville?" 'All the trains take five hours, ma'am, either way,' replied the official. ' And how many trains shall I meet on the way?' This absurd question tickled the guard, but he wa3 ready with his reply: ' A train leaves Wurzletown for Mudville, and also one from Mudville to Wurzletown, at five minutes past every hour. Perhaps the gentleman will oblige by working out the answer to your question,

as we are just off. Right away!' I certainly worked out tho answer; but when I got out of the train an hour later the silly old lady was as perplexed as ever in trying to understand why the number I gave her was correct. 'I don't believe Ft,' she said. 'I am going on a visit to my.son, who is a policeman, and I shall ask him. He is sure to know.' " This puzzle amused the children very much, and they were soon pushing raisins and almonds across the tablecloth from point to point, and tying their young brains into knots. THE MOTOR CAR FARE. "Woll, children, I broke my journey at Addleford, and hired a motor car to take me out to Clinkerville, where I had a sick aunt. In passing through the village of Bakenham, just midway between Addleford and Clinkerville, who should I meet but my old friend Watkins ? I agreed to take him on to Clinkervillo and bring him back to Bakenham on my return journey. Watkins is an eccentric fellow, and he insisted on paying his fair share of the hire. As I paid £3 myself for the car, what was the correct portion of the fare that Watkins should have contributed?" Most of the party tripped up over this very simple little question. THE CIRCULAR RAILWAY.

M It seemed as if there was to be ho end to my bewilderment. When I had settled down comfortably in the train for London I took up a magazine that I had bought, and thought I would let my fancy roam away into the land of But on the , first page at which I opened it I was-©on-

fronted with this puzzle." Here Simon brought out the magazine in question, and showed them the illustration that we reprint. "I read it, and. got fascinated with the thing. I made a large diagram on a sheet of paper, and cut out seven little pieces, which I numbered and used as counters. It was only just as we were running into Euston that I found the solution, and I must admit the time had passed very quickly. This is the puzzle: " The dark ring shews the main line of a circular railway and the other lines are loop lines. The counters, numbered 1 to 7, are trains at the stations, and one station is unoccupied. It is required to move the trains, one at a time, along the lines until they occupy the same stations in reverse order. That is, 1 must be where 7 is, 2 where 6 is, and so on. But only one train .can ever be at a station at the same time. I soon found a way of reversing the trains, but a condition is that you must do it in as few as 15 moves. That is where the trouble comes in. Make diagrams for yourselves, and use numbered counters. You will find it a fascinating puzzle." CHRISTMAS TREE PRESENTS. "When I got to London," resumed Mr Binks, "where I was breaking the journey for the night, I went round to see my old friend Bradgate. His family were preparing a large Christmas tree for a number of poor children in their district, and I found they wanted some small toys to complete it. So I went to a shop and bought 60 little articles for five shillings. All the wooden toys cost threepence each, all the toys made of tin cost twopence each, and every packst of sweets cost a halfpenny each. Now, as I bought just five times as many tin toys as wooden, I wonder whether you can tell how many there were of each kind to make up the exact money." THE FAMILY PARTY. "The Bradgates told me they were having a family gathering for the festive season. It was to consist of one grandfather, one grandmother, two fathers, two mothers, four children, three grandchildren, one brother, two sisters, two sons, two daughters, one father-in-law, one mother-in-law, and one daughter-in- " Quito a large party, said one of the company, who had been making notes on a piece of paper. "There were 23 persons in all." ~ "No; you are quite wrong, said Simon. "There were only seven persons altogether. Can you tell me how this could have been?" MAKING THE DRAUGHTS BOARD. "While I was waiting at Winkleton Junction for the local train to bring me on here," said Mr Binks, "I became interested in two schoolboys who were evidently going horns for the holidays. They seemed to be worried over a piece of what appeared to be linoleum, like this"—and he made a sketch which we reproduce in the illustration. "I was curious to know what their trouble was, and I asked them to tell me.

" ' Harold and I,' said one of the boys, ' wanted to play draughts in the tram, but we could not find a board, so our master gave us this piece of stuff and said that as it contained exactly 64 squares we could cut it into pieces and, by laying them together, make a very good board. We said it would be very awkward to play on, as the squares were nob chequered—black and white. Then he said that to keep us amused ha would give us a shilling each when wo came back to school if we could cut it along the lines into two pieces that would fit together and form a perfect square. So, instead of playing draughts, he set us worrying over this blessed puzzle.' " Naturally, I wanted to help the boys in their dilemma, and, do you know, it was one of the most interesting posers out of the many that I have had to perplex me this season. Can you find out how to cut it into the two pieces to form a square board?" EXTRACTING THE WINE. At this point in the proceedings, as the journalist- puts it, Mr Smiley was asking for a corkscrew to open a bottle of wine. " Half a moment," said Mr Binks, as he requested his host to pass him the bottle. " Here is another little puzzle. Can you tell me how I can extract the wine from this bottle without pulling the cork, without making a hole in it, and without breaking or piercing the bottle?" They all thought that this was quite impossible, but Mr Binks convinced them next morning that it was the easiest thing in the world. A CHARITABLE DISTRIBUTION. " Well, to resume my story," he went on, "while I was walking yesterday, a number of mta, who seemed to me really deserving of help, appealed to me for assistance. I had a certain amount of looso cash in my pocket (13s 9d to be exact), and I said I would divide it equally amongst them. As, in doing this, I found it absolutely necessary to give at least six coins to every man, you will find it a little perplexing to discover from that fact exactly how many men there were to share the gift." THE COW LN THE GARDEN. In concluding his perplexing stories, Mr Simon Binks produced the rough sketch plan that we give, and stated that it represented his square plot of ground, with his house at the bottom right-hand corner, and the stables at the lop lefthand corner. Then ho gave this queer account:

" After the snowstorm three weeks ago, when the country round me was* covered two or three inches deep in a white mantle, someone had left the gate open, as I have shown it, and while I was seated at breakfast with a friend a stray cow rushed in and began tearing around.. I ran out of the house and shut the gate, to keep others out, and afterwards got over the fence at B, where I am seen running. My friend joined in thepursuit, and climbedf the fence at F. Then my man, who was in the stables, also saw the animal, and dashed straight for the fence at M, where he climbed over. But the cow broke through the fence at the place shown, and got right away. " Now. I found afterwards that neither I, my friend, the man, nor the cow had ever crossed one another's tracks in the snow. I wonder which of yon can mark with a pencil the directions taken by all foui—myself, my friend, my man, and the cow?" Nobody succeeded in finding any solution to this, and they all waited with curiosity to see the answer next morning. SOLUTIONS TO PUZZLES. CARRYINGTHE BAGS. Lot the boy continue to carry one bag for one mile and a-third; then hand it to Mr Binks, whe will carry it to the station. Also let the nan carry his bag two miles and two-thirds, and then deliver it to the boy, who will carry it for the remaining distance. Then each pi the

three persons will have carried one bag two miles and two-thirds—an equal division of labor. THE STATION MASTER'S REPLY. The answer to Mr Binks's inquiry as to how long he had to wait was: "Two to two to 2.2." That is, four minutes. WHAT THE GUARD SAID. As the journey takes five hours, divide the route into five equal distances. Now, when the lady leaves Wurzletown there are four trains on the way and a fifth just starting. Each of these five she will meet. Also, when she has gone a mile, another will start, at two miles another, at four mileß another, and when she arrives nt Mudville a train will be just on the point of starting. If .we assume she does not " meet" this one. or meet the one that arrived at Wurzletown just as she left, she will have met altogether nine trains on the journey. MOTOR CAR > FARE. As Watkins only shares the car for half the journey, he should pay half 30s, or 15s. THE CIRCULAR RAILWAY. Move the trains in the following order. As there is never more than one station vacant there can be no uncertainty about the moves: 1, 7, 1, 2, 4, 5, 1, 6, 2, 6, 1, 5, 5, 4, 6. And the trains are reversed in order in the required 15 moves. CHRISTMAS TREE PRESENTS. Mr Binks must have bought 3 wooden toys at 3d each; 15 tin toys at 2d each; and 42 bags of sweets at id each. Thus he would obtain 60 articles for ss, and would buy five times as many tin as wooden toys. THE FAMILY PARTY. The party consisted of two little girls and a boy, their parents, and their father's father and mother. These seven individuals produce all the relationships mentioned. MAKING THE DRAUGHTS BOARD.

The illustration shows how to cut into two parte, A and B, that will fit together and form the square board. EXTRACTING THE WINE. All that is necessary is to push the cork in! A CHARITABLE DISTRIBUTION. There are 660 farthings in 13s 9d. Now, the possible divisors of 660 are 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60,66,110,132,165,220,330,660. There is only one of these values in farthings (165) that cannot be paid in fewer than six coins. Therefore, Mr Binks must have given 3s 5Jd to each of four men. THE COW IN THE GARDEN. The illustration shows ths tracks of Mr Binks, his friend, his manservant, and the cow. When Mr Binks closed the gate he swung across on it to the other side of the cow's track. Thus he did not cross her track "in the snow," but in the air. This

quibble of Mr Binks reminds us that we have often wondered whether, when a railway forbids you to " cross the line " at a station, you do not really do so by passing underneath it in the subway. You cannot get to the other side without crossing it above or below. But Mr Binks's solution is quite sufficiently good for a Christmas puzzle.

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