The Puzzle: 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' .4.5.6.7.8.9.0. which would add up to 82

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.