Talk:Verbal arithmetic

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[edit] Which Vatriquant?

Some web pages (including a couple of French ones) give "Maurice Vatriquant" or "M. Vatriquant" as the true name of Minos, the coiner of the name "crypt-arithmetique". However Don Knuth and David Singmaster give "S. Vatriquant". Who is right? Both?
Jorge Stolfi 06:50, 24 May 2004 (UTC)

[edit] Usefulness of casting out nines

I don't see the usefulness of casting out nines for solving alphametics, at least 2-addend ones. For example, in SEND + MORE = MONEY, M, O, S and R are solved in short order. The casting out nines rule then gives you E + D - Y + 1 = 0 mod 9. But this constraint doesn't give you anything that the right-most column doesn't. In general, casting out nines gives you equations with too many variables. Other techniques are much more helpful:

  • mod 10 arithmetic
  • treating columns as simultaneous equations
  • carry analysis
  • parity

Unless other types of alphametic puzzles get more mileage out of casting out nines, I'm inclined to remove its mention as an effective technique, and point the reader at techniques that work a little better.
JamesMayfield 19:33, 3 November 2006 (UTC)

  • Right you are. However, writing the equations modulo p, for prime numbers p, gives additional hints about the solution. This is a common method for solving diophantine equations. --Jorge Stolfi 11:39, 23 October 2007 (UTC)

[edit] Cryptic Sudoku and Kakuro

I removed this sentence because I could not make sense out of it:

Examples are variants of Sudoku and Kakuro in which clues are given in terms of cryptic alphametics such as NUMBER+NUMBER=KAKURO which has a unique solution 186925+186925=373850. Another example is SUDOKU=IS*FUNNY whose solution is 426972=34*12558.

In Sudoku, the numerical value of the digits is irrelevant; they are just nine different symbols, that cannot be repeated in the same row, column, or block. In Kakuro, the clues are sums of digits along each entry. In either casse, I don't see how clues to the solution are given using cryptarithms.
This same sentence has been inserted in the Sudoku and Kakuro articles, but it is not explained there either.
I propose to just mention the possibility in this article, and put the examples and explanation in the Sudoku and/or kakuro pages, as approrpiate. --Jorge Stolfi 11:39, 23 October 2007 (UTC)