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Verbal Arithmetic

by Centaur
Yesterday on the Chicago Cubs message board where I am “clarkstreet”, a poster presented a verbal arithmetic problem in post #11 (spoiler alert): http://www.forums.mlb.com/n/pfx/forum.aspx?tsn=1&nav=messages&webtag=ml-cubs&tid=405417 . Actually it was devised in 1924 by Henry Dudeney. The solution can be found on the internet, but I chose to first write a short computer program, and in a fractional second of running time found the unique solution. Then I learned more at Wikipedia (spoiler alert): http://en.wikipedia.org/wiki/Verbal_arithmetic

The challenge is to substitute unique decimal numerals for the letters in a phrase, and find the unique solution to a mathematical equation. No leading zeroes. The 1924 entry was:

SEND + MORE = MONEY

Since I had written a related computer program, I attempted to compose similar problems. Most either had no solution or multiple solutions. Finally I devised the following which has a unique solution. As far as I know it is original, so the internet is not likely to help:

BASE + BALL = GAMES

See if you can find the answer before the Dark of the Moon. ;)
in topics:

  • BASE + BALL = GAMES

    Select text below to see solution:

    7483+7455=14938
    - Sarawak, 2 years ago
  • Select text below to see solution:

    7483+7455=14938

    Well done, Coelacanth. Now its your turn to compose a verbal arithmetic problem. :clap:
    - Centaur, 2 years ago
  • Bugger. Now I have to improve my software (the version I produced was very specific to this problem). Or figure out a less brute-force method to solve these kinds of problems.

    Will take a little time . . .
    - Sarawak, 2 years ago
  • This one has two solutions.

    KILL+BILL=MOVIE
    - Sarawak, 2 years ago
  • I'd never be able to make one of these, but I got:
    9366+5366=14732
    After one false start.
    - Tog, 2 years ago
  • I'd never be able to make one of these, but I got:
    9366+5366=14732
    After one false start.

    Tog, that's one of the two solutions to Coelecanth's puzzle. The other solution is almost identical except the two addends switch places.

    Nice try, Coelecanth, but can you develop one with a single solution?
    - Centaur, 2 years ago
  • Nice try, Coelecanth, but can you develop one with a single solution?

    Geez, not good enough? Alright, I'll try another.

    Either you have a much more powerful computer than I do, or a much more efficient algorithm (or both), because mine takes quite a lot of seconds. I'll need to work on it.
    - Sarawak, 2 years ago
  • I received an e-mail indicating that a member was proposing a verbal arithmetic problem: STAR + WRIT = WRATH. There are no solutions. When I clicked the e-mail to go to the post, it refused to load. Apparently the poster withdrew the problem after realizing it had no solution.
    - Centaur, 2 years ago
  • Some of you may remember when my username was GrapeOfWrath, so I've incorporated that into a sort of CSI version of the puzzle:

    STAB + WRIT = WRATH

    ETA: Yes, Curt, I was attempting an astronomy/Hollywood/BAUT tie-in, and realized that I was too ambitious. :)
    - grapes, 2 years ago
  • STAB + WRIT = WRATH



    That's better, Grapes. Below is the unique solution in white.

    9567 + 1085 = 10652
    - Centaur, 2 years ago
  • Here's one about imperial succession:

    KITH + KILL = MIGHT
    - grapes, 2 years ago
  • Here's one about imperial succession:

    KITH + KILL = MIGHT

    Below in white:
    7483 + 7455 = 14938
    - Centaur, 2 years ago
  • Are you using a program to solve them, or just create them?
    - Tog, 2 years ago
  • Are you using a program to solve them, or just create them?

    Are you asking Coelecanth, Grapes or Centaur?

    I wrote a program that quickly solves the verbal arithmetic puzzles. I can also test meaningful phrases that I devise by inputting them into my program. The output shows all of the possible solutions. I only publish one if it has a unique solution.
    - Centaur, 2 years ago
  • Everyone, I guess. If you solve them by hand, about how long does it take?
    - Tog, 2 years ago
  • Everyone, I guess. If you solve them by hand, about how long does it take?
    Depends upon the problem. For

    SEND + MORE = MONEY

    it's pretty easy to see that the M has to be a 1, since the sum of two four-digit numbers can't be greater than 19998, and it can't be a leading zero. Since S+M has a carry, S must be a 9, or an 8 (with a carry from the E+O), and MO is either 10 or 11, but that means O is either 1 (which is already taken by M) or zero, so O is zero. O+E results in N, but since O is zero, there must have been a carry, and N=E+1 (E is not 9 because that would imply N is zero). Not only that, but O+E can't produce a carry, which means S is 9.

    We only have to check ENs of 23, 34, 45, 56, 67, 78, and that's just a little more work. We only have to find D, R, and Y, and we're done. :)
    - grapes, 2 years ago
  • No, I get how to solve them. The two I did took about ten minutes with a pad and paper, I'm just wondering how my ten minutes compares overall.

    Also, I was wondering if there would be any interest in tackling a couple of cyphers (in a different thread) that I want to put into a story. I need them to be casual reader proof, but I'm worried that they might be too easy to crack for the puzzle crowd.
    - Tog, 2 years ago
  • Tog, that's one of the two solutions to Coelecanth's puzzle. The other solution is almost identical except the two addends switch places.

    Nice try, Coelecanth, but can you develop one with a single solution?

    I've got my software down to where it solves short ones in a fraction of a second, but this is a lot harder than I thought it would be!
    - Sarawak, 2 years ago

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