# Talk:Verbal arithmetic

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## 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)

## 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)

## 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)

## Send More Money alignment

The alignment using pre tags is off, for me (using firefox, linux). (see this screenshot at right, taken from this diff).

Is there a way to achieve this sum that displays consistently across browsers? I've tried looking at Help:Math, but couldn't prod the examples into working here... -- Quiddity (talk) 20:35, 9 February 2010 (UTC)

Does this work for you:
${\begin{matrix}&&S&E&N&D\\+&&M&O&R&E\\\hline =&M&O&N&E&Y\\\end{matrix}}$ Gandalf61 (talk) 10:06, 10 February 2010 (UTC)
The alignment looks fine but the italic font is not so good. I tried \texttt but the wikimath will not recognise it. What about just
       S E N D
+ M O R E
-----------
= M O N E Y

The frame is ugly but that is a problem in many articles. All the best, --Jorge Stolfi (talk) 13:06, 10 February 2010 (UTC)
Gandalf's example is aligned perfectly, Jorge's example is the same as the old one (for me).
(I don't think any solution using <pre> is going to work reliably cross-browser. This new example is aligned the same for me as my screenshot of the current (except for the underlining), and can be fixed (for me) with the same removal of 2 spaces from the "+ M O R E" line).
(I just checked, and I have not accidentally mis-set my monospace font in firefox prefs ;)
Hopefully Gandalf can fix the italic/font in his solution? -- Quiddity (talk) 20:31, 10 February 2010 (UTC)
Well, \text produces a non-italic font - how's this:
${\begin{matrix}&&{\text{S}}&{\text{E}}&{\text{N}}&{\text{D}}\\+&&{\text{M}}&{\text{O}}&{\text{R}}&{\text{E}}\\\hline =&{\text{M}}&{\text{O}}&{\text{N}}&{\text{E}}&{\text{Y}}\\\end{matrix}}$ Gandalf61 (talk) 09:35, 11 February 2010 (UTC)
Perfect. I'll add it now. Revert (or fix/improve) if there's a problem :)
Hopefully that works for everyone - I tried the various math-rendering options in Special:Preferences, and it seemed to display the same for me in all of them. -- Quiddity (talk) 21:06, 11 February 2010 (UTC)

## Logic issues in sample problem

Second step for solving sample puzzle in the article says: "To produce a carry from column 4 to column 5, S + M is at least 9, so S is 8 or 9, so S + M is 9 or 10, and so O is 0 or 1. But M = 1, so O = 0."

Last sentence is not really well explained, it should mention the fact that O≠M — Preceding unsigned comment added by Dlougach (talkcontribs) 12:32, 27 June 2011 (UTC)

I figured out an extra way to solve this, suprised no-one has said this,

S=2,E=8,N=1,D=9,R=6,O=3,M=0, Y=7.

SEND+MORE = MONEY, 2819+0368=03187.

can someone confirm this at all? i am 17 btw :P, and it was fun to solve this, because son-one seems to say this way.

) i don't have a wiki account, but my name is Peter :3

Usually in these sorts of problems 0 is not allowed as the first digit of a number, because that's not the way you would normally write it (you would write 368, not 0368). —David Eppstein (talk) 22:33, 16 May 2013 (UTC)

## Reverse

"Reverse cryptarithm: A rare variation where a formula is written and the solution is the corresponding cryptarithm whose solution is the formula given."

I have no idea what this means; a given arithmetic problem can be framed in millions of ways. No examples or references are given. A web search turned up nothing sensible. I suggest this be deleted unless someone can provide examples. — Preceding unsigned comment added by Fomalhaut~enwiki (talkcontribs) 02:40, 5 December 2018 (UTC)

Presumably it's harder to frame the problem using English words than using nonsense sequences of letters. But this whole section is unsourced and should be removed unless sources can be found. —David Eppstein (talk) 02:57, 5 December 2018 (UTC)