Dissection of Rectangle into 9 Distinct Integral Squares

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): $9$
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