1972 AHSME Problems/Problem 33
Problem 33
The minimum value of the quotient of a (base ten) number of three different non-zero digits divided by the sum of its digits is
Solution
The answer we are looking for can be expressed as . This is equivalent to . Because we are trying to minimize our solution, we set = , so we have . This is equal to , which simplifies to . Since each digit is unique, we set to , leaving us with . Clearly, should be minimized, so and our answer is