Common Mistakes in the British Mathematical Olympiad

Errors in Reasoning and Presentation

• Making an unproven assumption. Explicitly state every claim and provide a proof for it, unless it is a standard, named theorem.
• Checking a few small cases and concluding a general pattern. Use small cases for intuition, but build a formal proof (e.g., by induction) for the general case.
• Writing a long explanation without clear logical steps. Structure your argument. Use phrases like 'We claim that...' and 'It remains to show...' to guide the marker.
• Ignoring edge cases, like division by a variable that could be zero. Always consider special cases. For example, if a proof involves 1/(n-1), handle the case n=1 separately.
• Stating the final answer without showing how it was reached. The solution is the argument itself. The final numerical answer is worth very little on its own.
• Misusing standard theorems, like applying AM-GM to non-positive numbers. Before applying any theorem, verify that all its conditions are met by the problem's constraints.