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Framing...
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.

Practice Problem

Find the sum of all positive factors of 72.72.

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.

Practice Problem

What is the sum of the positive factors of 360=23325?360 = 2^3 \cdot 3^2 \cdot 5?

Reframing a problem is also used in Combinatorics.

Practice Problem

How many ways are there to divide 55 indistinguisable candies among 33 distinguishable friends?

Practice Problem

How many ways are there to divide 55 indistinguisable candies among 33 distinguishable friends such that each friend must receive atleast 11 candy?