Cryptarithms

September 3, 2008 11:44 PM

   MEFI
   META
+ ASKME
-------
 FILTER

Each letter corresponds to a number 0-9. The solution is unique.

A cryptarithm (or alphametic) is a puzzle in which each digit of an equation is replaced by a different letter. One of the first, and best known, appeared in 1924:

  SEND
+ MORE
------
 MONEY

A collection of classic cryptarithms can be found here; some interesting extensions to the concept can be found here. And, if you'd like to make your own, the alphametic generator here and solver here may be of use.

posted by Upton O'Good (27 comments total)

That 'interesting extensions' link is fantastic. Great post! And great presentation, too.
posted by painquale at 11:55 PM on September 3, 2008

Cool. Here's a cached version of the geocities link.
posted by carsonb at 11:56 PM on September 3, 2008

The Alphametic Applet solved it instantly. Impressive.
posted by tellurian at 12:41 AM on September 4, 2008

A = 8
E = 4
F = 1
I = 0
K = 6
L = 3
M = 7
R = 2
S = 9
T = 5

darn
posted by Blazecock Pileon at 12:42 AM on September 4, 2008

"Alphametic"

Write it down, Darling. I like it. I want to use it more often in conversation.
posted by Dumsnill at 1:43 AM on September 4, 2008

Wow, the entire site of Mike Keith's is wonderful. I recognize his constrained pastiches of Poe, so I must have visited at least part of the site before, but a lot of the material seems new to me.
posted by painquale at 1:51 AM on September 4, 2008

Man, I loved those Sideways Arithmetic from Wayside School books when I was in elementary school. They were nothing but these kind of puzzles. They were fun but pretty tough when they started rolling in multiplication and division towards the back.
posted by Punkey at 2:14 AM on September 4, 2008 [1 favorite]

The symbol system is irrelevant to the solution of these kinds of problems.

I'd love to see an alphametic that used symbols combining into emoticons. That would be something.
posted by twoleftfeet at 2:45 AM on September 4, 2008

Oh, I've got one:

  :)
+ ;)
____
 :-)

Not great though. (Not a unique solution at all.) Ideally it should hang together like SEND + MORE = MONEY. But it is a new kind of puzzle!
posted by twoleftfeet at 3:08 AM on September 4, 2008

    THIS
+WILLNOT
--------
 WENDELL

posted by wendell at 3:47 AM on September 4, 2008 [1 favorite]

Another one:

   -->
+  <>

(Unique solution!) Not enough people awake making up alphametics.  (What? You got something better to do?)

posted by twoleftfeet at 3:59 AM on September 4, 2008

Apparently Metafilter's parsers get nervous if you type hyphen-hyphen-> (since that's the end escape for HTML). The problem (unique solution!) was <-hyphen-hyphen + hyphen-hyphen->= ??!

It's actually not a bad problem. Sorry for the formatting issue. (And it's not necessary to escape inside PRE, by the way.)
posted by twoleftfeet at 4:14 AM on September 4, 2008

  WHAT
   THE
+ FUCK 
------
  MATT

(Solvable, not uniquely, in base 10.)
posted by Wolfdog at 5:28 AM on September 4, 2008 [1 favorite]

If you do these puzzles in base 2, most of them are unsolvable. (One letter per digit, right?)
posted by twoleftfeet at 5:51 AM on September 4, 2008

Since no one else has posted it so far, I may as well go first and claim my special prize/compensation for being cruelly distracted at work.

***SPOILER SOLUTION***

MEFI
6310

META
6359

ASKME
94863

FILTER
107532
posted by leibniz at 6:42 AM on September 4, 2008

The world's smallest alphametic! (Where are the people from Guinness when you need them?):

  I
+ I
 ----
 ME

Rastafari!
posted by twoleftfeet at 7:08 AM on September 4, 2008

Hmm, I'm not sure if I should deserve credit for this or not:


SOLUTION
M = 2
E = 1
F = 0
I = 7
T = 8
A = 6
S = 9
K = 5
L = 3
R = 4
MEFI = 2107
META = 2186
ASKME = 69521
FILTER = 73814
posted by Perplexity at 7:22 AM on September 4, 2008

Moral of the story: When using Geocities, always upgrade to their 1 MB per month bandwidth plan.
posted by crapmatic at 7:46 AM on September 4, 2008 [1 favorite]

I first tried to mix some colors, but that didn't turn out to well. So I started asking some questions instead and finally got an answer:

WHY + WHEN + WHERE + WHO + HOW = ANSWER
posted by Timeless at 7:46 AM on September 4, 2008

Cryptarithm is the perfect goth-nerdcore band name.
posted by roger ackroyd at 8:47 AM on September 4, 2008 [1 favorite]

Unique solution in base 10:

   LOL
  FAIL
   LOL
  FAIL
   LOL
+ FAIL
------
 PALIN

posted by Wolfdog at 8:57 AM on September 4, 2008 [3 favorites]

Leading zeroes are generally excluded in this type of puzzle, Perplexity.
posted by DevilsAdvocate at 8:58 AM on September 4, 2008

I remember my jubilant introduction to these from Sideways Arithmetic at Wayside School! Thanks!
posted by Ambrosia Voyeur at 11:19 AM on September 4, 2008 [1 favorite]

I always found these from Sideways Arithmetic at Wayside School. They are lots of fun. They have a kind of quality which I also find in sudoku, but with some extra rules from mathematics which means you can put some logic into it.
posted by jamuraa at 12:08 PM on September 4, 2008

Unique solution in base 10:

  YUMMY
   SEXY
  MUSKY
-------
 VIXENS

posted by Wolfdog at 1:40 PM on September 4, 2008

It's funnier to solve them when you swap the letters for (non-solution digits).

E.g., solve this mentally:

    8427
 +  8453
   31684
 ---------
  279540

posted by qvantamon at 9:37 PM on September 4, 2008

Punkey: Not that you'll probably see this, but I happened to run across Sideways Arithmetic From Wayside School at the local thrift store today, and picked it up based on you mentioning it. I thought it would be appropriate for my middle school aged siblings, but, looking through it, I'll have to try my hand at the latter portion of the book.
posted by niles at 6:30 PM on September 8, 2008