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

This theorem requires a proof. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Sources

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