Can you place numbers from the range $[0,16]$ into a $2 \times 4$ grid such that all orthogonal pairwise differences are distinct? In other words, we want every pair of numbers that lie in the same row or in the same column to have a distinct difference. Good luck!
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asked Jun 3, 2021 at 7:46
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$\begingroup$ the question is not clear...how do you make the difference on the column where there are 4 numbers? $\endgroup$– MariusJun 3, 2021 at 8:02
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1$\begingroup$ The differences are computed only for pairs of numbers, where both numbers lie in the same row or in the same column. I tried to clarify the question. $\endgroup$– Dmitry KamenetskyJun 3, 2021 at 8:03
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2 Answers
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Here is one example
0 3 14 16
7 11 2 1
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$\begingroup$ Correct! By the way, this shows that the $2 \times 4$ rook graph is graceful. $\endgroup$ Jun 3, 2021 at 8:50
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I expect there are many. e.g.
0 3 15 16
0 11 5 7
