“Skeletons” or “arithmetical restorations” are said to have been invented in India, in the Middle Ages. These “restorations” were the fad in the first decades of the 20^th century.

Here is an example of "arithmetical restoration":

     Sphinx - Jan 1933 - Page 7
     By M. Pigeolet

      Reconstruct the multiplication, in which all the A=3 are given.

                    . . . . . A
                  A . . . . . .           
                 ---------------
                  A . A . A . J
                  . . . . . A
              . . . A . . N
              . . . A . V
          . A . . . . I
        . . . . . A E
      J A N V I E R
     ---------------------------
      . . . . . . . . . . . . .           

 

Compared to the modern cryptarithm genres they look bulky, awkward and are very tough to solve.

How those old fellows tackled this? Well, they knew much more about arithmetical theorems, divisibility, decimal fraction periodicity, etc. than we do nowadays. That´s why we find it difficult to tackle these old huge puzzles. Today everything has to be fast, simple and elegant in order to get some attention!

The book “150 Puzzles in Crypt-Arithmetic” written by Maxey Brooke in 1963 (Dover Publications Inc.) is the best source of information to solve “restorations”. It shows the step by step solutions to, say, 25 of these problems, most of them taken from journal Sphinx.

The book Mathematical Recreations and Essays by W.W. Rouse Ball and H.S.M. Coxeter (Dover Publications Inc.- 13th edition - ISBN 0-486-25357-0) also gives some basic theoretical principles used to decipher arithmetical restorations (pages 20 to 26).