Plot twist that catches people off guard: you can have the right idea and still lose points. Because in an olympiad, solving the problem in your head isn’t enough — you have to prove it on paper, in a way a judge who doesn’t know you can follow without guessing what you meant.
The Difference Between “I Solved It” and “I Proved It”
Having the right answer isn’t the same as having a complete solution. An olympiad solution has to justify every step: not “just because,” not “it’s obviously true,” but an argument the judge can follow without having to take your word for it.
“The judge isn’t inside your head. If your solution doesn’t convince them on paper, it doesn’t matter how clear it was to you.”
The Most Common Writing Mistakes
- Skipping “obvious” steps. What’s obvious to you isn’t always obvious to the judge — and an unjustified jump can cost you points even if the final result is right.
- Writing the discovery process instead of the proof. Your scratch work full of guesses and dead ends isn’t your final solution — the final solution is the clean path, once you already know where you’re going.
- Not defining what each symbol or variable means before using it, leaving the reader to guess.
- Asserting instead of proving. “It’s easy to see that…” doesn’t replace the argument — if it’s that easy, write it in one line and move on.
A Structure That Works
- State what you’re going to prove, in one sentence, before you start proving it.
- Go step by step, each one resting on the previous one or on a known fact.
- Mark the ending clearly — a “therefore, this is proven” (or the classic QED) tells the judge you got there.
What If My Reasoning Was Messy at First?
Doesn’t matter. Nobody grades your thought process, they grade what you wrote. Once you know the path, write it up clean, as if you’d never doubted it — even if it took you 40 minutes to find it.
Writing a good solution is a separate skill from solving the problem — and like any skill, it’s trained. Practice writing out full solutions to problems you already know how to solve: you’ll be surprised how many “obvious steps” weren’t actually so obvious. And once the writing is solid, what’s left is pure speed — that’s what we cover in mental math tricks to save seconds.