#math trivia #232 solution

There are at least three answers:

  • 232 = 2^3*29 (i.e., 8*29, where 2^3 is two cubed, or 8)
  • 232 = 203+29
  • 232 = 25321

Solving problems like this one usually requires a little trial and error.

To start with, we know that the last blank must be filled in with a digit; it wouldn’t make sense for the equation to end with a symbol.

The second blank must therefore be filled in with an operator, otherwise the equation would end with a four-digit number.  None of the operators applied to 2 and a four-digit number would yield 232 as a result.

Given these observations, the next step is to look for two-digit numbers starting with 2 that have a relationship with 232 given one of the operators.  One of them is 29, which is a divisor of 232.  Conveniently, its cofactor, 8, can be expressed as 2^3, leading to the first answer.

What about an answer using addition?  We’d like a two-digit number ending in 9, so that when added to a three-digit number ending in 3, the result ends in 2.  The two-digit number is again 29, and the three-digit number is 203.

The third answer involves subtraction.  Following similar logic, the two-digit number must end in 1, and the three-digit number is 232.

Are there any other solutions?  A little more trial and error will tell.

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