IMC 2012
contestants 316 · problems 10 (5+5) · 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 | 9.7 | 97% | 1% | 0.13 | combinatorics | ||
| P2 | hard | 3.5 | 18% | 24% | 0.58 | linear algebra | ||
| P3 | hard | 2.5 | 17% | 66% | 0.49 | games & processesgroup theory | ||
| P4 | killer | 0.2 | 0% | 95% | 0.25 | real analysis | ||
| P5 | killer | 0.5 | 2% | 91% | 0.28 | polynomialsnumber theory | ||
| Day 2 | ||||||||
| P6 | easy | 8.8 | 81% | 2% | 0.34 | games & processespolynomials | ||
| P7 | medium | 4.7 | 31% | 28% | 0.26 | sequences & series | ||
| P8 | hard | 2.4 | 22% | 71% | 0.55 | number theory | ||
| P9 | very hard | 1.9 | 10% | 75% | 0.47 | sequences & serieslinear algebra | ||
| P10 | killer | 0.0 | 0% | 100% | 0.16 | combinatoricsgroup theory | ||
A diploma-cohort cell needs at least 5 scores, else it shows “—”. How these statistics are computed →