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.
★ Full worked sample paper available — read it →
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.
★ Full worked sample paper available — read it →
2023
A
Dandelions: Friend? Foe? Both? Neither?
Spatial population growth + multi-factor "impact factor" for invasive species.
★ Full worked sample paper available — read it →
2022
A
The Need for Bees (and not just for honey)
Compartmental ODE for colony dynamics + pollinator-demand for a crop parcel.
★ Full worked sample paper available — read it →
2021
A
Storing the Sun
Pair a 100 MW solar plant with battery / pumped-hydro / thermal storage; LP dispatch + LCOS sweep.
B
Tackling the Drought
Lake Mead reservoir mass balance with Markov inflows; recommend shortage-tier policy.
2020
A
The Best Summer Job
Rank competing job offers; textbook AHP + TOPSIS with Monte Carlo sensitivity.
B
Funding Biodiversity Conservation
Allocate a fixed budget across Florida threatened plants; 0/1 knapsack with recovery probability.
2019
A
Charge!
Forecast US EV adoption + plan public charging-network; logistic growth + set-cover on interstates.
B
Bottle Battles
Campus single-use bottle policy; compartmental flow model + behavioural substitution.
2018
A
Roller Coaster
Objective ranking from a 300+ coaster dataset; EWM + TOPSIS with feature engineering.
B
Cozy Smart House
Smart climate-control schedule; lumped RC thermal model + LP optimization over comfort/cost/IAQ.
2017
A
Drone Clusters as Sky Light Displays
Choreograph hundreds of illuminated drones; perception-driven sampling + Hungarian assignment with layered-altitude deconfliction.
B
Ski Slope
Lay out runs and lifts on a DEM; shortest-path run routing + M/M/c lift queueing with on-slope density safety check.
2016
A
Swim, Bike, and Run
Wave-start triathlon scheduling for 2,000 athletes; pace-distribution fitting + clustering into waves + discrete-event congestion sim under a 5.5-hour road-closure cap.
B
Shop and Ship
Continental warehouse siting for one-day ground shipping; greedy set cover on county centroids + state sales-tax overlay + apparel-vs-gear re-solve.
2015
A
Preventing Road Rage
Late vs. early lane-merge under a 2→1 closure; Nagel–Schreckenberg CA simulation with a behavioral merge rule, plus a 3→1 extension and a secondary-road comparison.
B
City Crime and Safety
Two-week police-report dataset for a 2.8M-person city; composite safety index (incidence + severity + clearance) with AHP/EWM weights and DBSCAN hotspots.
2014
A
Unloading Commuter Trains
1D platform agent sim with density-dependent walking speed, M/G/c stair queues from Fruin capacities, k-center stairway placement under a footprint budget.
B
The Next Plague?
300-person village outbreak; SEIR + severity decision table on (R0, CFR, doubling) + LP for vaccine/antiviral/bed allocation under staged info drops.
2013
A
Emergency Medical Response
Place 3, then 2, then 1 ambulance across six zones to maximize 8-minute coverage; MCLP, integer programming, catastrophe analysis.
B
Bank Service Problem
Empirical arrivals + service times; meet wait < 2 min and queue ≤ 2; M/G/c simulation and minimum-staffing optimization.
2012
A
American Elk
Stage-structured Lefkovitch matrix + stochastic PVA for the Great Smoky Mountains reintroduction; rank management interventions and write a Wildlife Commissioner letter.
B
How Much Gas Should I Buy This Week?
Causal one-week-ahead forecast on EIA weekly retail gasoline prices + deadband full-vs-half rule, 2012 out-of-sample plus a major-city replication.
2011
A
No More Space Shuttles
Ten-year ISS resupply & crew strategy after STS-135; multi-period integer program over Soyuz/Progress/ATV/HTV/Dragon/Cygnus with redundancy and docking-port constraints.
B
Search and Find
Nighttime penlight search of a wooded park; sweep-width / lateral-range model, parallel-track pattern, small-object vs. lost-jogger scenarios under a time budget.
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.