I feel like there's some maths in this mistake I just made: I split a huge poster into a 6 × 3 grid of A4 pages, arranged like this:
\[ \begin{array}{cccccc} 1&4&7&10&13&16 \\ 2&5&8&11&14&17 \\ 3&6&9&12&15&18 \end{array} \]
I made the mistake of printing double-sided. I want to salvage as much as possible. I can't make up two rows, but I can do every other column.
What's the biggest contiguous area I can do?

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I can do a "comb" -
1,4,5,7,10,11,13,16,17
or
2,3,6,8,9,12,14,15,18.
Any others?

@christianp You can do a similar sort of comb with the middle row:
2,3,5,8,9,11,14,15,17
or
2,4,5,8,10,11,14,16,17.

@icecolbeveridge so I think my question is, for a m × n grid, with m sufficiently large, how many different maximal contiguous areas can you make? Should have a simple answer, I think - some kind of parity argument?

@christianp @icecolbeveridge the parity isn't dead.. it's just pining for the fjords.

.. I'll get my coat.

@CopernicusCF what sits on your shoulder and squawks 'pieces of seven! pieces of seven!'

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