Framing Problems
How to frame (or reframe) a problem to make it easier to solve.
Author: Jaden Park
One of the most important problem solving skills for math contests is figuring out how to make a problem easier to solve.
Find the sum of all positive factors of
Now, obviously, if there were more than 2 factors, we can't use a multiplication grid. However, we can use this same strategy to more dimensions.
What is the sum of the positive factors of
Reframing a problem is also used in Combinatorics.
How many ways are there to divide indistinguisable candies among distinguishable friends?
How many ways are there to divide indistinguisable candies among distinguishable friends such that each friend must receive atleast candy?