Dissection of Rectangle into 9 Distinct Integral Squares
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Theorem
Let $R$ be a rectangle.
Let $R$ be divided into $n$ squares which all have different lengths of sides.
Then $n \ge 9$.
The smallest rectangle with integer sides that can be so divided into squares with integer sides is $32 \times 33$.
Proof
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Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $9$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $9$