IMC 2000
contestants 117 · 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 | 66% | 5% | 0.65 | real analysis | ||
| P2 | easy | 6.2 | 50% | 21% | 0.66 | polynomials | ||
| P3 | medium | 5.4 | 45% | 33% | 0.58 | linear algebra | ||
| P4 | hard | 4.7 | 22% | 26% | 0.62 | inequalitiessequences & series | ||
| P5 | hard | 3.9 | 25% | 39% | 0.59 | abstract algebra | ||
| P6 | very hard | 1.3 | 5% | 68% | 0.47 | sequences & seriesreal analysis | ||
| Day 2 | ||||||||
| P7 | medium | 6.8 | 47% | 11% | 0.61 | combinatoricsgeometry | ||
| P8 | easy | 6.2 | 55% | 25% | 0.57 | real analysis | ||
| P9 | easy | 5.5 | 53% | 32% | 0.65 | polynomialscomplex analysis | ||
| P10 | medium | 4.6 | 35% | 36% | 0.66 | integrationpolynomials | ||
| P11 | very hard | 2.6 | 9% | 54% | 0.53 | functional equations | ||
| P12 | hard | 2.5 | 18% | 68% | 0.52 | linear algebra | ||
A diploma-cohort cell needs at least 5 scores, else it shows “—”. How these statistics are computed →