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 ![\[\boxed{\textbf{(C) }10.5}.\]](http://latex.artofproblemsolving.com/b/f/3/bf323353fef2c50fdebc25406cd8e303ccb739cf.png)
