Dr MATHS with Steve Humble Cryptarithmetic or Alphametic puzzles are mathematical problems in which each digit is replaced by a letter.
In the 20th century Alphametic puzzles became very popular, appearing in a range of newspapers and magazines.
Like all good Alphametic puzzles, the letters make words that form a meaningful phrase.
An alphametic, as most Word Ways readers are surely aware, is a puzzle like SEND + MORE = MONEY, in which letters are to be replaced with decimal digits to make a valid addition sum.
Since alphametic composers generally prefer puzzles which have a unique solution (i.
There are four types of two-addend alphametic, with the words having N, N, and N letters, or N, N, N+1, or N, N+1, N+1, or N, N+1, N+2.
No (14,14,14) or (13,13,14) or (13,14,14) or (12,13,14) alphametics were found--indeed, no alphametic having even a single 14-1etter word.
I came across this alphametic variant recently in correspondence with Zoran Radisavljevic, a wordplay enthusiast in Serbia, who showed me this wide example of the form composed in Croatian:
The goal here is to first solve the alphametic, which must by necessity have a unique solution, and then back-substitute letters for the digits in the cryptoclue to get the final answer, a word or phrase, which in this case is TROPSKA KLIMA, Croatian for "tropical clime".
The answer to Zoran's challenge is "yes", since several of the (13,13,13) alphametics listed above can be extended to a (13,13,13)+13 alphametic-plus-cryptoclue puzzle.
A special case of narrative alphametics are doubly-true alphametics, in which the narrative consists of a correct arithmetical statement, such as THREE + FOUR = SEVEN, with the solution 28566 + 7495 = 36061.
The following narrative alphametics have unique solutions and are soluble by hand without excessive enumeration (although in some cases they may require quite a bit of analysis).