Once you have understood the problem, you must decide how to tackle it. It is the most creative phase, and also the most uncomfortable: often you do not know where to start. Here are some techniques that help you to “get unstuck”.
Property — Five techniques to get unstuck
- Start from the simple case. If the general problem seems too big, try with small numbers, with , with a symmetric figure. Often what you see in the simple case extends to the general one.
- Reason backwards. Start from the thesis: to obtain this, what would be enough for me? Then: to obtain that “what”, what would be enough for me? Until you connect back to the data.
- Look for a similar problem already solved. Have you already seen something of the kind? A theorem that has the same form? A figure that appears under the same conditions?
- Introduce something. An unknown, an auxiliary segment, a coordinate system, a name for an angle. Often the path only opens up after you have added a new element.
- Formulate a conjecture. You do not have to be sure: write “I think it holds that…” and then try to verify it on a case. If it falls, you will have learnt something anyway.
Links
Topics: Working method
Concepts: Particular case · Conjecture · Backward reasoning · Solving strategy
Skills: Reasoning by cases