# Problem solving

## Subtleties in a Radical Limit Problem

(A new question of the week) I find it interesting to observe the process of problem-solving, particularly for proofs: how we discover a solution initially, and then how we turn that into a final answer. Sometimes we can see the main idea in a flash, but the process of writing it as a formal proof …

## Many Ways to Solve a Proportion

Last week we looked at a set of special rules for working with proportions, which have been largely replaced by the more general “tool” of algebra (the “Swiss army knife” of problem solving, which can do the job of many specialized tools), though the latter can still be useful. We still find that many students …

## Proportions vs. Algebra in Proofs

A new question of the week A simple question about the Basic Proportionality Theorem (which goes by several other names, including Thales’ Theorem) and its relationship to similar triangles leads to some helpful ideas about how to choose a suitable manipulation at each step in a proof, a skill central to good problem solving. In …

## Impossible? Try anyway!

(An archive question of the week) Here’s a little problem with some big lessons for problem solving. Not enough equations? This question is from Kenanga in 2017, not long before the Ask Dr. Math service stopped taking questions: Insufficient Information In Question Given A + B + C = 1 B + C + D …