IMC 2020
contestants 546 · problems 8 (4+4) · 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 | 7.7 | 70% | 11% | 0.29 | combinatorics | ||
| P2 | medium | 5.1 | 45% | 38% | 0.37 | linear algebra | ||
| P3 | killer | 0.1 | 1% | 98% | 0.22 | geometrycombinatorics | ||
| P4 | very hard | 0.7 | 6% | 92% | 0.34 | polynomialsinequalities | ||
| Day 2 | ||||||||
| P5 | medium | 5.0 | 35% | 26% | 0.40 | real analysis | ||
| P6 | hard | 1.9 | 16% | 72% | 0.45 | number theorypolynomials | ||
| P7 | very hard | 0.8 | 6% | 91% | 0.48 | group theory | ||
| P8 | killer | 0.1 | 0% | 98% | 0.16 | sequences & seriesreal analysis | ||
A diploma-cohort cell needs at least 5 scores, else it shows “—”. How these statistics are computed →