IMC 2001
contestants 185 · 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 | 9.0 | 88% | 5% | 0.23 | combinatorics | ||
| P2 | medium | 6.7 | 45% | 10% | 0.41 | group theory | ||
| P3 | hard | 2.8 | 20% | 62% | 0.43 | sequences & seriesintegration | ||
| P4 | killer | 0.3 | 2% | 95% | 0.32 | polynomialsnumber theory | ||
| P5 | very hard | 1.5 | 7% | 74% | 0.48 | linear algebra | ||
| P6 | very hard | 2.6 | 10% | 45% | 0.44 | real analysis | ||
| Day 2 | ||||||||
| P7 | very hard | 2.3 | 12% | 57% | 0.23 | polynomials | ||
| P8 | very hard | 3.4 | 14% | 24% | 0.27 | sequences & series | ||
| P9 | hard | 2.3 | 16% | 66% | 0.48 | geometrycombinatorics | ||
| P10 | very hard | 1.2 | 7% | 75% | 0.44 | linear algebra | ||
| P11 | killer | 1.4 | 3% | 63% | 0.30 | functional equationsreal analysis | ||
| P12 | killer | 0.5 | 4% | 94% | 0.13 | inequalitiesreal analysis | ||
A diploma-cohort cell needs at least 5 scores, else it shows “—”. How these statistics are computed →