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 20th century.
Here is an example of "arithmetical
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. Thatīs
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).