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Paco2004 Posted 21 years ago
Jokes, Puzzles & Riddles

Alphametic quiz

Hello people

I'm an English learner from Japan. Today I have questions not about the English language but about arithmetic, which I have found in a homework website for grade four kids. Here are the questions.

Each letter in each question stands for a 1-digit number. In each question, no two letters may stand for the same number. Two separate problems are unrelated. Find a value for each letter. (The sign * means 'multiplied by').
(1) ***=SNORE (Use the numbers: 6, 2, 0, 8, 4, 1, 3, and 9)
(2) ***=BRAND (Use the numbers: 1, 2, 4, 9, 3, 7, 8, and 5)
(3) ***=BULLET (Use the numbers: 1, 8, 6, 0, 5, 9, 2, and 4)

I have got the answers by using an almost try-and-error method. But the method takes really a lot of time:nearly 3 hours for each. Does anyone know the smartest way to solve this kind of alphametic quiz?

paco
  

Top answer

the brute force "try-and-error" is a good technique because you will always get all of the possible answers. the only down side of this algorithm is that is has O(n^2) time complexity. in fact, no matter what algorithm you use, this problem cannot be solved in better than O(n^2) time.

— Bigchris

  • the brute force "try-and-error" is a good technique because you will always get all of the possible answers.
  • the only down side of this algorithm is that is has O(n^2) time complexity.
  • in fact, no matter what algorithm you use, this problem cannot be solved in better than O(n^2) time.
  • if someone presented me with this problem, i would immediately implement this algorithm (brute force) with a simple computer program.
  • it's really the simplest systematic way of doing this.
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6 Answers
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the brute force "try-and-error" is a good technique because you will always get all of the possible answers. the only down side of this algorithm is that is has O(n^2) time complexity. in fact, no matter what algorithm you use, this problem cannot be solved in better than O(n^2) time.

if someone presented me with this problem, i would immediately implement this algorithm (brute forc
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Oh! thank you for your reply. I'm sorry to be too late to find your reply. I never thought anyone would reply. Yes we can solve the problem by computing out simultaneous equations under constraints that variables differs each other and less than 10. But you know these are given as homework for grade four kids! I can't believe it!

The answers I got by the try-error method were as follow
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Hi Big Chris,

Just for your next quiz:
you can also notice that either E is 0 or Y is 1 (since *** = E in the one's place).


This is not true:

BE * IT = LIE
32 * 16 = 512

Here for the one digit it is also: *** = E but neither E = 0 nor T = 1.

Also are you sure about the O(n^2) ? This would be an excellent algorithm
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Hey paco,

If your kid gets more homework of this kind use this link (requires Java on your PC):

http://www.geocities.com/CapeCanaveral/Campus/7705/metic/metic.html

Solutions for TIE * TRY = SNORE found this URL:

190 * 182 = 34580
180 * 1
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Thank you for that great link. Im helping my neighbor with his homework and we have been working on the same problem for over an hour using guess work. Thanks again
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I need help with this problem. MENTAL+HEALTH=MATTERS
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