IMC 1999
contestants 87 · 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 | medium | 5.5 | 33% | 8% | 0.46 | linear algebrapolynomials | ||
| P2 | medium | 5.4 | 47% | 39% | 0.64 | sequences & seriescombinatorics | ||
| P3 | easy | 6.5 | 62% | 32% | 0.51 | functional equations | ||
| P4 | medium | 4.1 | 31% | 43% | 0.71 | functional equations | ||
| P5 | medium | 5.5 | 48% | 33% | 0.58 | combinatorics | ||
| P6 | killer | 0.1 | 0% | 97% | 0.22 | real analysisinequalities | ||
| Day 2 | ||||||||
| P7 | easy | 7.5 | 74% | 22% | 0.25 | abstract algebra | ||
| P8 | medium | 5.6 | 49% | 32% | 0.58 | probabilitycombinatorics | ||
| P9 | hard | 3.7 | 29% | 53% | 0.54 | inequalities | ||
| P10 | medium | 3.9 | 31% | 44% | 0.67 | functional equationsinequalities | ||
| P11 | killer | 0.3 | 0% | 90% | 0.41 | abstract algebracombinatorics | ||
| P12 | killer | 0.4 | 2% | 91% | 0.30 | number theorycombinatorics | ||
A diploma-cohort cell needs at least 5 scores, else it shows “—”. How these statistics are computed →