167.—­THE WIZARD’S CATS.

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A wizard placed ten cats inside a magic circle as shown in our illustration, and hypnotized them so that they should remain stationary during his pleasure.  He then proposed to draw three circles inside the large one, so that no cat could approach another cat without crossing a magic circle.  Try to draw the three circles so that every cat has its own enclosure and cannot reach another cat without crossing a line.

168.—­THE CHRISTMAS PUDDING.

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“Speaking of Christmas puddings,” said the host, as he glanced at the imposing delicacy at the other end of the table.  “I am reminded of the fact that a friend gave me a new puzzle the other day respecting one.  Here it is,” he added, diving into his breast pocket.

“‘Problem:  To find the contents,’ I suppose,” said the Eton boy.

“No; the proof of that is in the eating.  I will read you the conditions.”

“’Cut the pudding into two parts, each of exactly the same size and shape, without touching any of the plums.  The pudding is to be regarded as a flat disc, not as a sphere.’”

“Why should you regard a Christmas pudding as a disc?  And why should any reasonable person ever wish to make such an accurate division?” asked the cynic.

“It is just a puzzle—­a problem in dissection.”  All in turn had a look at the puzzle, but nobody succeeded in solving it.  It is a little difficult unless you are acquainted with the principle involved in the making of such puddings, but easy enough when you know how it is done.

169.—­A TANGRAM PARADOX.

Many pastimes of great antiquity, such as chess, have so developed and changed down the centuries that their original inventors would scarcely recognize them.  This is not the case with Tangrams, a recreation that appears to be at least four thousand years old, that has apparently never been dormant, and that has not been altered or “improved upon” since the legendary Chinaman Tan first cut out the seven pieces shown in Diagram I. If you mark the point B, midway between A and C, on one side of a square of any size, and D, midway between C and E, on an adjoining side, the direction of the cuts is too obvious to need further explanation.  Every design in this article is built up from the seven pieces of blackened cardboard.  It will at once be understood that the possible combinations are infinite.

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The late Mr. Sam Loyd, of New York, who published a small book of very ingenious designs, possessed the manuscripts of the late Mr. Challenor, who made a long and close study of Tangrams.  This gentleman, it is said, records that there were originally seven books of Tangrams, compiled in China two thousand years before the Christian era.  These books are so rare that, after forty years’ residence in the country, he only succeeded in seeing perfect copies of the first and seventh volumes with fragments of the second.  Portions of one of the books, printed in gold leaf upon parchment, were found in Peking by an English soldier and sold for three hundred pounds.