Digits with distinct pairwise sums

HardCombinatorics Brainteasers~8m

What is the largest $n$ for which there exists an $n$ -digit number whose digits are distinct and have all distinct pairwise sums? (For $n = 3$ , e.g. $174$ works since $1+7$ , $1+4$ , $7+4$ are all different.)

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Two disjoint pairs have equal sums exactly when they have equal differences.
A difference $d$ can appear at most twice (as a chain $x, x+d, x+2d$ ), and only once if $d \ge 5$ . Count how many pairs that allows.

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Digits with distinct pairwise sums

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