Is there any method by which I can tell whether a given alphametic is valid or not?


To validate a given alphametic, that is, confirm if it has a unique solution, the easiest way is to submit it to an alphametic solver (computer program).

In the Web you find four major online solvers:

  1. Jorge Soaresīs "Alphametic Puzzle Solver"

  2. Naoyuki Tamuraīs "Cryptarithmetic Puzzle Solver"

  3. Truman Collinsīs "Alphametic Puzzle Solver"

  4. Robert Israel's "The Alphametic Applet"

Solvers #1, #2 and #3 tackle additions only, whereas solver #4 solves 5 types of arithmetic operations: addition, subtraction, multiplication, division and exponentiation.

If you test the puzzle  TWO + MEN = MEET you will find that it is not a valid alphametic, because it has no solution.

If you test the puzzle BILL + GATES = GREAT you will find that it is not a valid alphametic, because it has 74 solutions.

But you can try testing PLACE + A + CALL = LATER and ... bingo! you find that this is a valid alphametic, which has got a unique solution: (67142 + 1 + 4177 = 71320).
  Back to Primer