Definition:Think of a Number/Historical Note

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Historical Note on Think of a Number

The think of a number puzzle goes way back in time.

Henry Ernest Dudeney discusses it in his posthumous ($1932$) collection Puzzles and Curious Problems as follows, presented on $\mathsf{Pr} \infty \mathsf{fWiki}$ as a 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 $120$.

He explains that:

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.

Note, however, that since Dudeney wrote the above, the Rhind Papyrus from was found to contain a number of examples of this puzzle.

This pushes the earliest date back to $\text {c. 1650}$ $\text {BCE}$, considerably earlier than Nicomachus.


Sources

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