Henry Ernest Dudeney/Modern Puzzles/105 - The Squares of Veneer/Solution

Modern Puzzles by Henry Ernest Dudeney: $105$

The Squares of Veneer

A man has two squares of valuable veneer, each measuring $25$ units by $25$ units.

One piece he cut, in the manner shown in our illustration, in four parts that will form two squares,

one $20$ units by $20$ units, and the other $15$ units by $15$ units.

Simply join $C$ to $A$ and $D$ to $B$.

How is he to cut the other square into four pieces that will form again two other squares, with sides in exact units,

but not $20$ and $15$ as before?

Solution

The required squares are $24$ by $24$ and $7$ by $7$.

Pieces $A$, $B$ and $C$ go to form the $24$ by $24$ square, while piece $D$ is the $7$ by $7$ square cut out intact.

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Solutions: $105$. -- The Squares of Veneer
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $329$. The Squares of Veneer