Toolbox
Some general suggestions for problem solving:
Some general suggestions for problem solving:
- Exploit Symmetry
- Work backward
- While counting, look at things from different angles and always try to exchange order of summation
- Try smaller problems, lower dimensions, extreme cases
General principles:
General principles:
- Pigeonhole principle (Dirichlet)
- Parity checks (odd vs. even)
- Apply arithmetic modulo N, remember your divisibility criteria
- Induction, strong induction
- Use of geometric transformations
Links:
Links:
Terry Tao on problem solving