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.
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Sources

  • 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $35$
  • 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $35$
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