IMC 2006
contestants 241 · problems 12 (6+6) · scale 0–20 · 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 | 9.2 | 88% | 1% | 0.39 | real analysis | ||
| P2 | easy | 7.1 | 54% | 18% | 0.51 | number theory | ||
| P3 | hard | 2.5 | 16% | 64% | 0.39 | linear algebranumber theory | ||
| P4 | very hard | 1.7 | 9% | 69% | 0.42 | polynomials | ||
| P5 | very hard | 1.4 | 11% | 80% | 0.31 | inequalitiesreal analysis | ||
| P6 | killer | 0.3 | 1% | 95% | 0.18 | real analysispolynomials | ||
| Day 2 | ||||||||
| P7 | easy | 9.2 | 88% | 3% | 0.35 | combinatoricsgeometry | ||
| P8 | easy | 8.2 | 76% | 4% | 0.41 | real analysisfunctional equations | ||
| P9 | very hard | 1.3 | 6% | 68% | 0.20 | real analysisinequalities | ||
| P10 | medium | 3.6 | 31% | 53% | 0.55 | linear algebra | ||
| P11 | medium | 3.8 | 35% | 55% | 0.53 | number theorypolynomials | ||
| P12 | killer | 0.0 | 0% | 99% | 0.16 | linear algebra | ||
A diploma-cohort cell needs at least 5 scores, else it shows “—”. How these statistics are computed →