39. Two bootmakers who lived in the town of B., thrown out of employment, resolved to go to G., a town 24 miles north from B., where there is a large factory; one of them went straight on to G., but the other went first to C., a small township west of B., and then went direct to G., his whole journey being 45 miles. What is the distance from C. to G.? 40. A tree which grows each year 1 inch less than the previous year, grew a yard in the first year; the value of the tree at any time is equal to the number of pence in the cube of the number of yards of its height. What is the value of the tree when done growing? THIS OFTEN “STICKS” PEOPLE UP. 41. What two odd numbers multiplied together make 7? MAGIC SQUARES. A Magic Square is a series of figures arranged in the equal divisions of a square in such a manner that the figures in each row when added up, whether horizontally, vertically, or diagonally, form exactly the same sum. They have been called “Magic” because the ancients ascribed to them great virtues, and because this arrangement of numbers formed the basis and principle of their talismans. Archimedes devoted a great amount of attention to them, which has caused a great many to speak of them as “the squares of Archimedes.” They may be either odd or even. When the former, the following method will be found valuable:-- With the digits from 1 to 25 form a square so that the numbers when added up horizontally, vertically, or diagonally will amount to 65. _Method._--Imagine an exterior line of squares above the magic square you wish to form, and another on the right hand of it. These two imaginary lines are shown in the diagram. 18 25 2 9 +----+----+----+----+----+ | 17 | 24 | 1 | 8 | 15 | 17 +----+----+----+----+----+ | 23 | 5 | 7 | 14 | 16 | 23 +----+----+----+----+----+ | 4 | 6 | 13 | 20 | 22 | 4 +----+----+----+----+----+ | 10 | 12 | 19 | 21 | 3 | 10 +----+----+----+----+----+ | 11 | 18 | 25 | 2 | 9 | +----+----+----+----+----+ 1st. In placing the numbers in the square, we must go in the ascending diagonal direction from left to right, any number which, by pursuing this direction, would fall into the exterior line must be carried along that line of squares, whether vertical or horizontal, to the last square. Thus, 1 having been placed in the centre of the top row, 2 would fall into the exterior square above the fourth vertical line; then ascending diagonally 3 falls into the square diagonally from 2, but 4 falls out of it to the end of a horizontal line, and it must be carried along that line to the extreme left and there placed. Resuming our diagonal ascension to the right we place 5 where the reader sees it, and would place 6 in the middle of the top row, but as we find 1 is already there we look for the direction to