### Question:

### 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.

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

### Answer:

###### 80+.5.+.97+.46 =82

###### It can also be written asĀ

###### 80+5/99+97/99+46/99 =80+198/99=82

###### The dot over a number signifies that it is a repeater which would go on for ever, eg 1/6 decimally as 0.6666 . . . . (etc)

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

So If a proper fraction is divided by 9s e.g. 46/99 is exactly equal to the numerator with the repeater sign followed by the decimal.