Common Mistakes on the USAMO
The USAMO tests not just mathematical knowledge but also rigor and clarity. Many points are lost to errors in reasoning and presentation, not just calculation.
Errors in Logic and Presentation
- Assuming the converse of a statement. Check if your logical implication works in both directions before claiming it does.
- Forgetting to check edge cases. Test your proof with n=1, prime numbers, or degenerate geometric configurations.
- Stating a result is 'obvious' or 'trivial'. Justify every step in your argument, no matter how simple it seems to you.
- Misstating or misusing a named theorem. Write down the precise conditions and conclusion of any theorem you use.
- Writing a disorganized or unreadable solution. Structure your proof with clear labels, definitions, and a logical flow.
- Giving up on a problem too early. Spend at least an hour on each problem; try small cases and re-read the question.