IMC 2023
contestants 393 · 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 | 7.7 | 72% | 6% | 0.46 | functional equationsreal analysis | ||
| P2 | easy | 7.0 | 65% | 23% | 0.27 | linear algebra | ||
| P3 | medium | 4.1 | 30% | 40% | 0.64 | polynomialsfunctional equations | ||
| P4 | killer | 1.0 | 3% | 82% | 0.41 | number theory | ||
| P5 | killer | 0.1 | 1% | 98% | 0.28 | combinatorics | ||
| Day 2 | ||||||||
| P6 | medium | 5.3 | 47% | 36% | 0.48 | games & processeslinear algebra | ||
| P7 | hard | 3.8 | 26% | 45% | 0.49 | real analysis | ||
| P8 | very hard | 2.1 | 14% | 59% | 0.52 | combinatoricsinequalities | ||
| P9 | killer | 0.7 | 1% | 73% | 0.41 | geometry | ||
| P10 | killer | 0.2 | 1% | 98% | 0.24 | number theorysequences & series | ||
A diploma-cohort cell needs at least 5 scores, else it shows “—”. How these statistics are computed →