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I was inspired by this great puzzle.

Can you place each number from 1 to 8 twice into a 2x8 grid, such that each pair of numbers $k$ are separated by Manhattan distance $k$?

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2 Answers 2

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Here is one of the possible answer:

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the first thing is to put

8, since it has to be the farest from each other. then 7, then 6.

The rest

it comes by itself instantly.

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    $\begingroup$ Nice work! It's similar solution that I got. $\endgroup$ Mar 29, 2023 at 12:09
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Swapping two adjacent and unequal numbers changes each number's part length by 1. Therefore, a Langford rectangle with n pairs is only possible if n and the n'th triangular number have the same parity - that is, if n is congruent to 0 or 1 modulo 4. Here are constructions yielding an infinite family for each remainder:

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