Part 9 (2/2)
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Another forram on a slate and then rub it out in three rubs
240--THE UNION JACK
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The illustration is a rough sketch so, the Union Jack It is not possible to draw the whole of it without lifting the pencil fro over the same line twice The puzzle is to find out just howyour pencil or going twice over the same line Take your pencil and see what is the best you can do
241--THE DISSECTED CIRCLE
Howyour pencil fron shown in our illustration? Directly you change the direction of your pencil it begins a new stroke You o over the same line more than once if you like It requires just a little care, or you may find yourself beaten by one stroke
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242--THE TUBE INSPECTOR'S PUZZLE
The man in our illustration is in a little dilemma He has just been appointed inspector of a certain systeularly, within a stated period, all the co twelve stations, as shown on the big poster plan that he is contee his route so that it shall take hi as possible He in where he likes and end where he likes What is his shortest route?
Could anything be simpler? But the reader will soon find that, however he decides to proceed, the inspector o over some of the lines more than once In other words, if we say that the stations are a mile apart, he will have to travel more than seventeen miles to inspect every line There is the little difficulty How far is he compelled to travel, and which route do you recommend?
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243--VISITING THE TOWNS
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A traveller, starting from town No 1, wishes to visit every one of the towns once, and once only, going only by roads indicated by straight lines How many different routes are there from which he can select? Of course, he must end his journey at No 1, from which he started, and ht froo the right way to work
244--THE FIFTEEN TURNINGS
Here is another queer travelling puzzle, the solution of which calls for ingenuity In this case the traveller starts froo as far as possible whilethe same road twice The towns are supposed to be a ht to A, then straight to B, then to C, D, E, and F, you will then find that he has travelled thirty-seven o in fifteen turnings?
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245--THE FLY ON THE OCTAHEDRON
”Look here,” said the professor to his colleague, ”I have been watching that fly on the octahedron, and it confines its walks entirely to the edges What can be its reason for avoiding the sides?”
”Perhaps it is trying to solve so it to start from the top point, how many different routes are there by which itthe sae in any route?”
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The proble at it during leisure ree--in fact, they were both wrong If the reader is surprised at their failure, let him attempt the little puzzle himself I will just explain that the octahedron is one of the five regular, or Platonic, bodies, and is contained under eight equal and equilateral triangles If you cut out the two pieces of cardboard of the shape shown in thethe dotted lines and then bend theether, you will have a perfect octahedron In any route over all the edges it will be found that the fly must end at the point of departure at the top
246--THE ICOSAHEDRON PUZZLE
The icosahedron is another of the five regular, or Platonic, bodies having all their sides, angles, and planes similar and equal It is bounded by twenty siles If you cut out a piece of cardboard of the for the dotted lines, it will fold up and form a perfect icosahedron
Now, a Platonic body does not mean a heavenly body; but it will suit the purpose of our puzzle if we suppose there to be a habitable planet of this shape We will also suppose that, owing to a superfluity of water, the only dry land is along the edges, and that the inhabitants have no knowledge of navigation If every one of those edges is 10,000and a solitary traveller is placed at the North Pole (the highest point shown), how far will he have to travel before he will have visited every habitable part of the planet--that is, have traversed every one of the edges?
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247--INSPECTING A MINE
The diagraalleries in a e, A to B, B to C, C to H, H to I, and so on, is one furlong in length It will be seen that there are thirty-one of these passages Now, an official has to inspect all of them, and he descends by the shaft to the point A How far must he travel, and what route do you recommend? The reader es, each a furlong in length, he will have to travel just thirty-one furlongs” But this is assue more than once, which is not the case Take your pencil and try to find the shortest route You will soon discover that there is roo puzzle
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248--THE CYCLISTS' TOUR
Two cyclists were consulting a road ether The circles represent towns, and all the good roads are represented by lines They are starting from the toith a star, andthere they want to visit every other town once, and only once That is the difficulty Mr Spicer said, ”I as replied, ”No way, I'm sure” Nohich of them was correct? Take your pencil and see if you can find any way of doing it Of course you must keep to the roads indicated
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249--THE SAILOR'S PUZZLE
The sailor depicted in the illustration stated that he had since his boyhood been engaged in trading with a s soh chart of which I have given a copy, and explained that the lines from island to island represented the only routes that he ever adopted He always started fro of the season, and then visited every island once, and once only, finishi+ng up his tour at the starting-point A But he always put off his visit to C as long as possible, for trade reasons that I need not enter into The puzzle is to discover his exact route, and this can be done with certainty Take your pencil and, starting at A, try to trace it out If you write down the islands in the order in which you visit them--thus, for example, A, I, O, L, G, etc--you can at once see if you have visited an island twice or onored--that is, you must continue your route direct, and you are not allowed to switch off at a crossing and proceed in another direction There is no trick of this kind in the puzzle The sailor knew the best route Can you find it?
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250--THE GRAND TOUR
One of the everyday puzzles of life is the working out of routes If you are taking a holiday on your bicycle, or a motor tour, there always arises the question of how you are to make the best of your tiet as far as some particular place, to include visits to such-and-such a town, to try to see so of special interest elsewhere, and perhaps to try to look up an old friend at a spot that will not take you much out of your way Then you have to plan your route so as to avoid bad roads, uninteresting country, and, if possible, the necessity of a return by the sa puzzle is attacked and solved I will present a little poser based on these lines
I give a rough map of a country--it is not necessary to say what particular country--the circles representing towns and the dotted lines the railways connecting them Now there lived in the townthe whole of his life had never once left his native place Fro incessantly to his trade, and had no desire whatever to roa his fiftieth birthday he decided to see so of his country, and especially to pay a visit to a very old friend living at the town marked Z What he proposed was this: that he would start from his home, enter every town once and only once, and finish his journey at Z As he rand tour by rail only, he found it rather a puzzle to work out his route, but he at length succeeded in doing so How did he et that every town has to be visited once, and not more than once
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251--WATER, GAS, AND ELECTRICITY
There are some half-dozen puzzles, as old as the hills, that are perpetually cropping up, and there is hardly ainquiries as to their solution Occasionally one of these, that one had thought was an extinct volcano, bursts into eruption in a surprising manner I have received an extraordinary nu the ancient puzzle that I have called ”Water, Gas, and Electricity” It is as, but the new dress brings it up to date The puzzle is to lay on water, gas, and electricity, from W, G, and E, to each of the three houses, A, B, and C, without any pipe crossing another Take your pencil and draw lines showing how this should be done You will soon find yourself landed in difficulties
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252--A PUZZLE FOR MOTORISTS
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EightTheir respective houses and churches, together with the only roads available (the dotted lines), are shown One went from his house A to his church A, another from his house B to his church B, another from C to C, and so on, but it was afterwards found that no driver ever crossed the track of another car Take your pencil and try to trace out their various routes
253--A BANK HOLIDAY PUZZLE
Two friends were spending their bank holiday on a cycling trip Stopping for a rest at a village inn, they consulted a route map, which is represented in our illustration in an exceedingly sih without all the original complexities They started from the town in the top left-hand corner marked A It will be seen that there are one hundred and twenty such towns, all connected by straight roads Now they discovered that there are exactly 1,365 different routes by which theyeither due south or due east The puzzle is to discover which town is their destination
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Of course, if you find that there are more than 1,365 different routes to a town it cannot be the right one