IMC 2021
contestants 589 · 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 | 7.4 | 69% | 11% | 0.39 | linear algebra | ||
| P2 | medium | 5.4 | 39% | 19% | 0.46 | probabilitycombinatorics | ||
| P3 | very hard | 1.3 | 8% | 80% | 0.50 | sequences & seriesreal analysis | ||
| P4 | killer | 0.1 | 1% | 98% | 0.21 | real analysis | ||
| Day 2 | ||||||||
| P5 | easy | 5.8 | 55% | 31% | 0.55 | linear algebra | ||
| P6 | hard | 2.3 | 17% | 71% | 0.57 | group theory | ||
| P7 | very hard | 0.9 | 6% | 92% | 0.42 | complex analysis | ||
| P8 | killer | 0.0 | 0% | 99% | 0.08 | linear algebracombinatorics | ||
A diploma-cohort cell needs at least 5 scores, else it shows “—”. How these statistics are computed →