Page:The Strand Magazine (Volume 72).djvu/682

666 as I liked so long as I did not lift my pencil from the paper. She assured me that it was quite easy—when you know how to do it. And as she showed me her method I was not disposed to contradict that statement.

walking down one of the streets of a favourite English seaside resort when I happened to run up against my old friend, Rackbraine, who was coming out of a fruiterer's shop with a small bag of peaches.

"Are peaches cheap to-day?" I asked him. For a moment or two he did not answer. Then he said, in his charactenistic way:—

"Well, you have to pay for six dozen peaches as many shillings as the man is selling peaches for thirty-two shillings. You may like to work out the price per peach?"

I was on a little tour in Italy, collecting material for my book on "Improvements in the Cultivation of Macaroni," I happened to be one day on the top of the Leaning Tower of Pisa in company with an American stranger. "Some lean!" said my companion. "I guess we can build a bit straighter in the States. If one of our skyscrapers in New York bent in this way there would be a hunt round for the architect."

I remarked that the point at which we leant over was exactly one hundred and seventy-nine feet from the ground, and he put to me this question: "If an elastic ball was dropped from here, and on each rebound rose exactly one-tenth of the height from which it fell, can you say what distance the ball would travel before it came to rest?" I found it a very interesting proposition.

was during my stay in Hong-Kong that O met a wily old Chinaman who first drew my attention to the remarkable possibilities of "Tangrams," which had been known to his countrymen for thousands of years. I tried with puzzle after puzzle that I could remember of the cutting-out class and failed to defeat him. He always seemed to be able to go one better. For example, I gave him the Greek cross, with which everybody to-day is familiar, and asked him to cut it into four pieces with two clips of the scissors so that they would fit together and form a square.

"No want two cuts," he said. "Do it in one." I said it was impossible, but, with an artful smile, he folded up the cross and then with one clip of the scissors produced his four pieces, which certainly fitted together and formed a perfect square. This I thought was so ingenious that I made a careful note of how it may be done. And yet it is not difficult if you give it a little thought, though I considered it too good to be left unrecorded.



man scored 50, 10, 5. 3, 2, 1, and another scored 25, 20, 20, 3, 2, 1, and the last scored 25, 20, 10, 10, 5, I

numbers that comply with the conditions must be cither of the form 81n+31 or 81n+50. The two smallest answers are 355 of the first form and 455 of the second. In the first case the square is 126025, which gives 14002+7, and in the second case the square is 207025, which divided by 9 gives 23002 and remainder 7. In both cases the digits of the quotient add to 7.

puzzle is quite impossible of solution, and here is my curious, but easy and convincing, proof. As there are no simple moves, but only leaps, those counter; that are on the squares marked A can only be transferred to the other squares marked A in its own system, and so with B, C, and D. Every counter must keep to its own system of sixteen squares, and can never pass into one of the other systems. Now, note that at the start we have three A's, three B's, three C's, and one D, while at the bottom corner we need to have one A, three B's, three C's, and three D's. To solve the puzzle it is therefore necessary that two counters moving on the A system should be transferred to squares on the D system, which is not possible, and therefore the thing cannot possibly be done. Now add two more counters on the D squares marked with stars, and mark the two A squares indicated by crosses as to be occupied at the end. Now, as we have three counters on every system at the start and in the final position, the thing is quite possible. In fact, it is so easy that the reader will then solve the puzzle without any trouble whatever.

words are:—

(1) ENTRANCE.

(2) DESERT.

(3) SUBJECTS.

(4) OBJECT.

in the following order: 12, 8, 4, 3, 2, 6, 10, 9, 13, 15, 14, 12, 8, 4, 7, 10, 9, 14, 12, 8, 4, 7, 10, 9, 6, 2, 3, 10, 9, 6, 5, 1, 2, 3, 6, 5, 3, 2, 1, 13, 14, 3, 2, 1, 13, 14, 3, 12, 15, 3—fifty moves in all.

In solution to 824, the numbers 567, 729, and 891 were inserted by mistake and 605 omitted. In 826, if we ignore the common practice of cancelling the 0, we can solve by 310)10174126840. 