Henry Ernest Dudeney/Puzzles and Curious Problems/141 - The First Boomerang Puzzle
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Puzzles and Curious Problems by Henry Ernest Dudeney: $141$
- The First "Boomerang" Puzzle
- You ask someone to think of any whole number between $1$ and $100$,
- and then divide it successively by $3$, $5$ and $7$,
- telling you the remainder in each case.
- You then immediately announce the number that was 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 mathematicians did it.
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Historical Note
In the words of Henry Ernest Dudeney:
- 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 by Nicomachus, who died about the year $120$.
Sources
- 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Various Arithmetical and Algebraical Problems: $141$. -- The First "Boomerang" Puzzle
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Miscellaneous Puzzles: $213$. The First "Boomerang" Puzzle