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In response to
"You're on the right track. -- nm"
by
znufrii
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OK I've got it now. (before I looked at your answer above) spoils -- (edited)
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Working off my initial assumption that the numbers were all base 8, I made a column of those values.
To the left and right of this, I did the same for bases 2-7 and 9-16. There were some holes in the columns for the lower digits since those weren't valid.
Looking at the resulting table, I saw a beautiful diagonal of 15's cutting across it from the bottom of the base 4 column to the top of the base 15 column.
Extending the line yields 120 (15 in base 3) and 1111 (15 in base 2).
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