# 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

## Sources

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $9$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $9$