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Pandigital Triangles

Published on Saturday, 9th March 2019, 07:00 pm; Solved by 224;
Difficulty rating: 40%

Problem 660

We call an integer sided triangle $n$-pandigital if it contains one angle of 120 degrees and, when the sides of the triangle are written in base $n$, together they use all $n$ digits of that base exactly once.

For example, the triangle (217, 248, 403) is 9-pandigital because it contains one angle of 120 degrees and the sides written in base 9 are $261_9, 305_9, 487_9$ using each of the 9 digits of that base once.

Find the sum of the largest sides of all n-pandigital triangles with $9 \le n \le 18$.