Henry Ernest Dudeney/Puzzles and Curious Problems/181 - Three Greek Crosses from One/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $181$

Three Greek Crosses from One

How can you cut a regular Greek cross into as few pieces as possible

so as to reassemble them into $3$ identical smaller regular Greek crosses?

Solution

Cut the upper and lower arms $A$ and $B$ off the Greek cross and lay them alongside the remainder to make a long rectangle.

Then cut the larger piece to get $C$, $D$ and $E$ and make the rectangle shown:

Then you cut that rectangle up as follows:

and hey presto.

Unconvincing.

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Historical Note

Martin Gardner reports that Harry Lindgren has discovered a $12$ piece dissection.

This appears in his $1964$ work Geometric Dissections.

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solutions: $181$. -- Three Greek Crosses from One
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $347$. Three Greek Crosses from One