Hexominoes cannot form Rectangle

Theorem

While there are a total of $210$ squares in a complete set of hexominoes, it is impossible to build them into a rectangle of side lengths $a$ and $b$ where $a \times b = 210$.

Proof

This theorem requires a proof. In particular: I'll have to check this, but I think the proof is along the lines that if you coloured them in a checkerboard pattern, you can't get an equal number of black and white squares. 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): $35$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $35$