Past problems archive
A curated walkthrough of recent HiMCM problems. Each problem page has the full prompt, the modeling approach top teams used, the key formulas, and what judges said in their commentary.
How to use this. Don't just read the outlines — open the original PDF (linked from each
problem) and try to write your own 5-page partial solution before reading our outline. Then
compare. That's how you actually learn to model.
The archive
2025 · 1,055+ teams · 20+ countries
A
Emergency Evacuation Sweeps
Multi-floor building sweep optimization; graphs, routing, simulation.
B
Environmental Impact of Sport Mega-Events
Recommend host cities for the Super Bowl by sustainability; multi-criteria decision.
2024
A
To Play or Not to Play: Modeling Future Olympic Games
Pick sports for Brisbane 2032; AHP / TOPSIS / EWM with sensitivity analysis.
B
Environmental Impact of High-Powered Computing
Model HPC carbon emissions; energy mix, logistic growth, multi-impact.
2023
A
Dandelions: Friend? Foe? Both? Neither?
Spatial population growth + multi-factor "impact factor" for invasive species.
B
Charging Ahead with E-buses
Plan a 10-year electric-bus transition; ecological + financial models combined.
2022
A
The Need for Bees (and not just for honey)
Compartmental ODE for colony dynamics + pollinator-demand for a crop parcel.
B
CO₂ and Global Warming
Fit multiple models to atmospheric CO₂ data; relate to land-ocean temperatures.
Older years (2018–2021, summarized)
| Year | Problem A | Problem B |
|---|---|---|
| 2021 | Storing the Sun (energy storage sizing) | Aluminum Can-undrum (recycling logistics) |
| 2020 | It's a Stretch! (resistance bands for fitness) | Driverless Vehicles in NJ Turnpike |
| 2019 | Carbon Sequestration in Forests | Substance abuse rehab planning |
| 2018 | Roller Coaster Capacity Planning | Cheap, Public Internet (network design) |
All older prompts are linked on COMAP's previous problems page.
Patterns across years
Reading 8+ problems back-to-back, certain templates show up over and over. Train for these.
| Pattern | Examples | Likely techniques |
|---|---|---|
| Pick the best X by multi-criteria scoring | 2025-B, 2024-A | AHP, TOPSIS, EWM (often combined) |
| Forecast a quantity over time | 2024-B, 2023-B, 2022-B | Regression, logistic growth, ARIMA, scenarios |
| Population dynamics / spread | 2023-A, 2022-A, 2019-B | ODEs, compartmental models, diffusion |
| Optimization / routing | 2025-A, 2021-A, 2018-A | LP/MIP, greedy heuristics, graphs, simulation |
| Quantify an environmental / social impact | 2025-B, 2024-B, 2023-A, 2022-B | Compositional models, indices, externality math |
| Plan a multi-year transition | 2023-B, 2024-B | Phased optimization, NPV financial models, scenario planning |
What every problem asks for
Reading the requirements lists carefully, almost every HiMCM problem has the same five-part skeleton:
- Understand the problem. Identify key factors / variables.
- Build the model on a simple baseline scenario.
- Apply to two or three more complex / varied scenarios.
- Extend the model — add realism, sensitivity, what-if.
- Communicate via a 1-to-2 page letter / blog / article to a non-technical stakeholder.
Once you see this skeleton, every problem becomes less intimidating.