66 Arithmetic & Algebraic Problems"I can do better than that," said Alec. "Let me take Bill as a partner, and
we will do the job for you in eight days."
Then how long would each man take over the job alone?- WORKING ALONE
Alfred and Bill together can do a piece of work in twenty-four days. If
Alfred can do only two-thirds as much as Bill, how long will it take each of
them to do the work alone?- THE FIRST "BOOMERANG" PUZZLE
One of the most ancient forms of arithmetical puzzle is that which I call
the "Boomerang." Everybody has been asked at some time or another to
"Think of a number," and, after going through some process of private
calculation, to state the result, when the questioner promptly tells you the
number you thought of. There are hundreds of varieties of the puzzle.
The oldest recorded example appears to be that given in the Arithmetica of
Nicomachus, who died about the year 120. He tells you to think of any
whole number between 1 and 100 and then divide it successively by 3, 5, and
7, telling him the remainder in each case. On receiving this information he
promptly discloses the number you thought of.
Can the reader discover a simple method of mentally performing this feat?
If not, he will perhaps be interested in seeing how the ancient mathematician
did it.
- LONGFELLOW'S BEES
When Longfellow was Professor of Modern Languages at Harvard College
he was accustomed to amuse himself by giving more or less simple arithmetical
puzzles to the students. Here is an example:
If one-fifth of a hive of bees flew to the ladamba flower, one-third flew to
the slandbara, three times the difference of these two numbers flew to an arbor,
and one bee continued to fly about, attracted on each side by the fragrant
ketaki and the malati, what was the number of bees?