56 Arithmetic & Algebraic ProblemsThat being so, can you say exactly how many men were in the hospital? It
is a simple calculation, but I have no doubt it will perplex many readers.
- A COW'S PROGENY
"Supposing," said my friend Farmer Hodge, "that cow of mine to have a
she calf at the age of two years, and supposing she goes on having the like
every year, and supposing everyone of her young to have a she calf at the age
of two years, and afterwards every year likewise, and so on. Now, how many
do you suppose would spring from that cow and all her descendants in the
space of twenty-five years?" I understood from Hodge that we are to count
from the birth of the original cow, and it is obvious that the family can pro-
duce no feminine beef or veal during the period stated.
- SUM EQUALS PRODUCT
"This is a curious thing," a man said to me. "There are two numbers
whose sum equals their product. That is, they give the same result whether
you add them together or multiply them together. They are 2 and 2, for if you
add them or multiply them, the result is 4." Then he tripped badly, for he
added, "These are, I find, the only two numbers that have this peculiarity."
I asked him to write down any number, as large as he liked, and I would
immediately give him another that would give a like result by addition
or multiplication. He selected the number 987,654,321, and I promptly wrote
down the second number. What was it? The fact is, no matter what number
you may select there is always another to which that peculiarity applies
in combination with it. If this is new to the reader it cannot fail to be inter-
esting to him. He should try to find the rule.- SQUARES AND CUBES
Can you find two whole numbers, such that the difference of their squares
is a cube and the difference of their cubes is a square? What is the answer in
the smallest possible numbers?
- CONCERNING A CUBE
What is the length in feet of the side of a cube when (1) the surface area
equals the cubical contents; (2) when the surface area equals the square of