The Magician's Own Book, or, the Whole Art of Conjuring / Being a complete hand-book of parlor magic, and containing over one thousand optical, chemical, mechanical, magnetical, and magical experiments, amusing transmutations, astonishing sleights and subtleties, celebrated card deceptions, ingenious tricks with numbers, curious and entertaining puzzles, together with all the most noted tricks of modern performers.

by George Arnold; Frank Cahill

THE SQUARE OF GOTHAM.

The wise men of Gotham, famous for their eccentric blunders, once undertook the management of a school; they arranged their establishment in the form of a square divided into 9 rooms. The playground occupied the center, and 24 scholars the rooms around it, 3 being in each. In spite of the strictness of discipline, it was suspected that the boys were in the habit of playing truant, and it was determined to set a strict watch. To assure themselves that all the boys were on the premises, they visited the rooms, and found three in each, or 9 in each row. Four boys then went out, and the wise men soon after visited the rooms, and finding 9 in each row, thought all was right. The four boys then came back, accompanied by four strangers; and the Gothamites, on their third round, finding still 9 in each row, entertained no suspicion of what had taken place. Then 4 more "chums" were admitted; but the clever men, on examining the establishment a fourth time, still found 9 in each row, and so came to an opinion that their previous suspicions had been unfounded. How was all this possible?

The following figures represent the contents of each room at the four different visits; the first, at the commencement of the watch; the second, when four had gone out; the third, when these 4, accompanied by another 4, had returned; and the fourth, when 4 more had joined them.

On each change the boys arranged themselves in the rooms in such a manner that, when the corner rooms were counted as a part of two rows, each entire row of three rooms contained the same number of boys. The illusion of the wise men was due to their mistake in counting each corner room twice.

THE MATHEMATICAL BLACKSMITH.

A blacksmith had a stone weighing 40 lbs. A mason coming into the shop, hammer in hand, struck it and broke it into four pieces. "There," says the smith, "you have ruined my weight." "No," says the mason, "I have made it better, for whereas you could before weigh but 40 lbs. with it, now you can weigh every pound from 1 to 40." Required size of the pieces?

Ans. 1, 3, 9, 27; for in any geometrical series proceeding in a triple ratio, each term is 1 more than twice the sum of all the preceding, and the above series might proceed to any extent. In using the weights, they must be put in one or both scales as may be necessary: as to weigh 2, put 1 in one scale, and 3 in the other.

CURIOUS PROPERTIES OF SOME FIGURES.

Select any two numbers you please, and you will find that one of the two, their amount when added together, or their difference, is always 3, or a number divisible by 3.