.4.5.6.7.8.9.0.
All the seven figures and the eight "dots" (see above) should be used to add up to 82.

Source: A famous $1000 prize problem that Sam Loyd issued in 1882.

  4   ⋅ 8.5     =   34
+ 6.0 ⋅ 7.9...  = + 48
=============    =====
                    82

In this solution, three dots are used as decimal points, two dots are used as dot operators, and three dots are used as an ellipsis to indicate the digit sequence following the decimal is a reptend.

I believe Sam Lloyd used the combined notations of the decimal point and overdot. The overdot is a substitute notation for the viniculum which is used to indicate a digit sequence is a reptend. As both the viniculum and overdot are difficult to represent in ASCII, I substitute these notations with the underline:

 80.5  =  80  5/9
   .46 =     46/99
+  .97 = +   97/99
======   =========
          82

Three dots are used as decimal points, and five dots are used as overdots over the five decimal digits.

Edited on January 24, 2016, 9:35 am

Posted by Dej Mar on 2016-01-24 09:26:29