— Burt Kaliski Jr. (@modulomathy) August 21, 2013
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 = 253–21
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.