Some puzzles goes as follows: Solve AB×B×A=BBB, where different letters denote different numbers and A and B are not zero.

What is the name for these types of puzzles?

Edit. I fixed my mistake in the puzzle, now it has solution.

  • 2
    $\begingroup$ Incidentally, that particular puzzle has no solution. $\endgroup$
    – dan04
    Nov 24, 2019 at 20:19
  • 1
    $\begingroup$ @dan04, thank you for comment, i have fixed the puzzle. $\endgroup$
    – Nick
    Nov 24, 2019 at 23:49

2 Answers 2


This is a type of puzzle called a "cryptarithm" or an "alphametic". We have many examples of this type of puzzle under the tag.


(And for completeness, the answer)

A=3, B=7. This is because BBB is divisible by 111, so we must have either 37 or 74 in any factorisation of BBB (37 is prime) into 1 or 2 digit numbers. Trying both, only AB=37 works.

  • 3
    $\begingroup$ The solution can be even simpler - first divide by B (since it's nonzero) to get AB*A=111, and the only factorisation of 111 is 37*3. $\endgroup$
    – trolley813
    Nov 25, 2019 at 8:56

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