The weight of a brick

Puzzle

Here is a little puzzle designed to illustrate the principle of cancellation as applied in algebra to discover an unknown weight from a fractional part of itself. As these kindergarten illustrations are given to instruct beginners in the rudimental principles of algebra, and not for the purpose of puzzling them, we present the explanation with the picture before them.
Algebra teaches us that the balance is not affected by removing similar quantities from both sides of an equation, so, in this puzzling little proposition we remove three-quarters of the whole brick and cancel off the three-quarter bat. This leaves the weight balancing with one-quarter of a brick; therefore if one quarter of a brick weighs three-quarters of a pound, a whole brick weighs three pounds. It suggests a possible solution to Uncle Jake's problem of the goose which weighed seven pounds and five-sevenths of its own weight. But then the goose always said there was no answer to the problem.
We almost lose veneration for the big fish story which for several centuries has been the terror of every graduating scholar. The head of the fish was nine feet long, the body as long as the head and tail together, and the tail as long as the head and half of the body. The head being a known quantity we find the length of the body to be 9 plus half of the tail.
The tail therefore equals 9 (the head) and half of 9 (41/2) which makes 131/2 added to half of itself.
Here is where the resemblance to the brick problem comes in. The tail is 131/2 feet long and half of itself. If one half equals 131/2, both halves equals 27 feet. Thus we have the length of the tail as 27 feet, and the body 36 feet, so 9 plus 36 plus 27 shows that Baron Muncausen must have landed a 72 foot fish, and he caught it with a hook.

References

• Loyd, Sam [1914]. in Loyd, Sam, Jr.: Sam Loyd's Cyclopedia of 5000 Puzzles Tricks and Conundrums (in English). New York: Lamb Publishing company, page 17.