IMC 2016
contestants 320 · 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 | 7.5 | 63% | 11% | 0.54 | real analysis | ||
| P2 | medium | 5.9 | 48% | 10% | 0.52 | linear algebra | ||
| P3 | easy | 6.0 | 56% | 35% | 0.45 | inequalities | ||
| P4 | very hard | 1.3 | 5% | 79% | 0.40 | combinatorics | ||
| P5 | killer | 0.3 | 2% | 96% | 0.29 | combinatoricsnumber theory | ||
| Day 2 | ||||||||
| P6 | easy | 7.0 | 56% | 10% | 0.42 | inequalitiessequences & series | ||
| P7 | easy | 6.6 | 55% | 18% | 0.58 | integrationinequalities | ||
| P8 | very hard | 2.1 | 10% | 62% | 0.38 | combinatoricsnumber theory | ||
| P9 | killer | 0.7 | 3% | 92% | 0.40 | combinatoricsinequalities | ||
| P10 | killer | 0.1 | 1% | 99% | 0.16 | linear algebrainequalities | ||
A diploma-cohort cell needs at least 5 scores, else it shows “—”. How these statistics are computed →