Elementary Lessons in Algebra.
To some people the itlea of adding a b c to x y z, or multiplying; letters together, seems the height of absurdity, and they fail to grasp the simplicity of algebra.
In the above puzzle we find a capital illustration of the principle of substitution and the adding of like quantities to both sides of an equation without affecting the equilibrium, so to speak, and an explanation of the reason for so doing to obtain other values. It shows the truth of the algebra axiom that "things which are equal to the same things are equal to each other."
In the first instance we see that a top and three cubes weigh equal to twelve marbles. In the second equation a top alone equals a cube and eight marbles. Now let us add three cubes to each side of the second scales, and as the addition of equal quantities to both sides of an equation does not change their relative values, we have the same equilibrium. By the addition of three cubes to the second pair of scales we have produced lhe identical values as shown by lhe first scales. In the first case a top and three cubes = twelve marbles; in the second illustration we have proved that a top and three cubes = four cubes and eight marbles; therefore if four cubes and eight marbles weigh the same as twelve marbles, four cubes = four marbles, so a marble weighs just as much as a cube. It proves therefore that one cube and eight marbles, or nine marbles weighs equal to the top!
The Catholic Church my first maintains ;
My next consists of poles and chains.
Distinctive whole—may'st thou ne'er brand
With foul disgrace our native land.
Cipher Answer.—13, 1, 19, 19, 1,3, 18, 5.
Add two-thirds of an inn to a couple of asses,
You'll then see a brute that all other surpasses.
Cipher Answer.— 1, 19, 19, 1,19, 19, 9, 14.
My first denotes a company, of any art or trade,
My second is a holy maid, whose vows to God are made;
My third, though hollow in the head, can make a wondrous sound,
My whole creates a cheerful laugh when mirth and wit go round.
Cipher Answer.— 3, 15, 14, 21, 14, 4, 18, 21, 13.
Here is an astronomical puzzle which is supposed to show the erratic path of the comet Heclai. Commencing with the small white star, show the shortest possible course through the exact center of all of the black stars so as to mark them all off and end with the big star.
In how few moves, in straight lines, could the comet Heclai destroy the entire constellation of sixty-two stars, beginning from and ending with the white stars?
The Astronomical puzzle solve by 14 straight lines.