Henry Ernest Dudeney/Puzzles and Curious Problems/141 - The First Boomerang Puzzle

by : $141$

 * 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.