Henry Ernest Dudeney/Modern Puzzles/115 - The Carpenter's Puzzle
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Modern Puzzles by Henry Ernest Dudeney: $115$
- 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,
- 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.
- If you move the piece marked $B$ up one step to the left,
- 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.
Click here for solution
Historical Note
Martin Gardner points out that Dudeney, in Problem $150$ in his Amusements in Mathematics, catches Sam Loyd out in exactly such a blunder.
He does this in 536 Puzzles & Curious Problems, his $1968$ repackaging of Dudeney's Modern Puzzles and Puzzles and Curious Problems.
Sources
- 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Geometrical Problems: Dissection Puzzles: $115$. -- The Carpenter's Puzzle
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Geometrical Problems: Dissection Puzzles: $338$. The Carpenter's Puzzle