Henry Ernest Dudeney/Modern Puzzles/115 - The Carpenter's Puzzle

by : $115$

 * The Carpenter's Puzzle
 * Here is a well-known puzzle, given in all the old books.


 * A ship's carpenter had to stop a hole $12$ inches square,
 * and the only piece of wood that was available measured $9 \ \mathrm{in.}$ in breadth by $16 \ \mathrm{in.}$ length.
 * How did he cut it into only two pieces that would exactly fit the hole?
 * The answer is based on the "step principle", as shown in the diagram.


 * Dudeney-Modern-Puzzles-115.png


 * If you move the piece marked $B$ up one step to the left,
 * it will exactly fit on $A$ and form a perfect square measuring $12$ inches on every side.


 * This is very simple and obvious.
 * But nobody has ever attempted to explain the general law of the thing.
 * As a consequence, the notion seems to have got abroad that the method will apply to any rectangle where the proportion of length to breadth is within reasonable limits.
 * This is not so, and I have had to expose some bad blunders in the case of published puzzles that were supposed to be solved by an application of this step principle,
 * but were really impossible of solution.$^*$
 * Let the reader take different measurements, instead of $9 \ \mathrm{in.}$ by $16 \ \mathrm{in.}$,
 * and see if he [or she] can find other cases in which this trick will work in two pieces and form a perfect square.