IMC 2007
contestants 243 · 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 | 9.7 | 97% | 0% | 0.16 | number theorypolynomials | ||
| P2 | easy | 7.0 | 55% | 7% | 0.49 | linear algebra | ||
| P3 | hard | 3.5 | 20% | 42% | 0.57 | linear algebrapolynomials | ||
| P4 | hard | 2.0 | 16% | 69% | 0.61 | group theorycombinatorics | ||
| P5 | killer | 0.6 | 4% | 94% | 0.48 | functional equationspolynomials | ||
| P6 | killer | 0.6 | 3% | 91% | 0.37 | polynomialscomplex analysis | ||
| Day 2 | ||||||||
| P7 | medium | 4.9 | 49% | 50% | 0.44 | real analysisgeometry | ||
| P8 | easy | 6.1 | 52% | 26% | 0.47 | number theory | ||
| P9 | easy | 5.4 | 51% | 40% | 0.44 | real analysistopology & metric spaces | ||
| P10 | hard | 2.2 | 17% | 72% | 0.47 | linear algebra | ||
| P11 | very hard | 0.9 | 8% | 89% | 0.55 | linear algebra | ||
| P12 | killer | 0.1 | 0% | 99% | 0.36 | polynomialsreal analysis | ||
A diploma-cohort cell needs at least 5 scores, else it shows “—”. How these statistics are computed →