IMC 2010
contestants 328 · problems 10 (5+5) · scale 0–10 · per-problem yesPer-problem difficulty
Day 1
Day 2
Difficulty vs discrimination
Each dot is one problem. X — how many solved it (scored ≥ 8 of 10); Y — discrimination, i.e. how well the problem told strong contestants from weak ones (score-vs-total correlation).
A good problem sits high and away from the edges. Bottom-left dots separated nobody — almost everyone failed them the same way.
Problem statistics
Same data as the Day 1 / Day 2 charts above. Add diploma cohorts to compare winners against the field.
| # | difficulty | all | disc | topics | ||||
|---|---|---|---|---|---|---|---|---|
| avg | solved | near-0 | ||||||
| Day 1 | ||||||||
| P1 | easy | 9.5 | 95% | 5% | 0.22 | integrationinequalities | ||
| P2 | medium | 5.4 | 37% | 19% | 0.51 | sequences & series | ||
| P3 | hard | 3.3 | 29% | 64% | 0.49 | sequences & series | ||
| P4 | very hard | 1.5 | 7% | 74% | 0.39 | number theory | ||
| P5 | killer | 0.3 | 2% | 97% | 0.29 | inequalities | ||
| Day 2 | ||||||||
| P6 | medium | 7.4 | 47% | 3% | 0.49 | sequences & seriesreal analysis | ||
| P7 | medium | 5.2 | 48% | 39% | 0.35 | inequalities | ||
| P8 | very hard | 1.2 | 7% | 85% | 0.40 | group theory | ||
| P9 | killer | 0.5 | 2% | 93% | 0.42 | linear algebracombinatorics | ||
| P10 | killer | 0.1 | 1% | 99% | 0.24 | functional equationsnumber theory | ||
A diploma-cohort cell needs at least 5 scores, else it shows “—”. How these statistics are computed →