Our Columbus Problem Puzzle - Solution

The Puzzle:

Our Columbus Problem
Here is a famous prize problem that Sam Loyd issued in 1882, offering $1000 as a prize for the best answer showing how to arrange the seven figures and the eight "dots" . which would add up to 82.

Out of several million answers, only two were found to be correct.

Our Solution:

The dot over a number signifies that it is a repeater which would go on for ever, as when we endeavor to describe 1/3 decimally as 0.33333 . . . . (etc)

With a series of numbers we place the dot over the first and last, as with 0.97979797979 . . . (etc)

The remarkable feature being that a proper fraction divided by 9s e.g. 46/99 is exactly equal to the numerator with the repeater sign followed by the decimal.
Puzzle Author: Loyd, Sam

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