IMC 2004
contestants 180 · 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 | 8.1 | 78% | 13% | 0.51 | set theory & logicreal analysis | ||
| P2 | easy | 8.0 | 69% | 4% | 0.29 | polynomialsreal analysis | ||
| P3 | medium | 5.5 | 38% | 28% | 0.72 | real analysis | ||
| P4 | medium | 4.0 | 35% | 52% | 0.52 | geometrycombinatorics | ||
| P5 | killer | 0.6 | 4% | 93% | 0.29 | combinatorics | ||
| P6 | killer | 0.4 | 1% | 90% | 0.27 | complex analysis | ||
| Day 2 | ||||||||
| P7 | easy | 7.9 | 72% | 15% | 0.47 | linear algebra | ||
| P8 | medium | 4.1 | 31% | 44% | 0.48 | integrationinequalities | ||
| P9 | easy | 5.4 | 51% | 41% | 0.52 | geometryinequalities | ||
| P10 | very hard | 1.6 | 6% | 75% | 0.52 | linear algebra | ||
| P11 | very hard | 1.1 | 9% | 84% | 0.21 | integrationinequalities | ||
| P12 | killer | 0.2 | 1% | 97% | 0.13 | linear algebracombinatorics | ||
A diploma-cohort cell needs at least 5 scores, else it shows “—”. How these statistics are computed →