The 37% rule for choosing the best: a maths EPQ idea
A title to start from
When should you stop looking? How well does the 37% rule work for choosing the best option?
Why it works as an EPQ
A neat result with a short proof, and real situations (flat hunting, hiring) where its assumptions can be tested.
Scope and difficulty
Solid. Solid. Prove the result, simulate it, then test what happens when the assumptions change.
The maths
Builds on these A Level topics: Probability · Sequences and series · Exponentials and logarithms · Integration.
You would learn:
- The secretary problem
- Approximating sums by integrals
- Simulation
One possible plan
- Set up the problem and find the best cut-off for small n by hand.
- Show the best cut-off tends to n/e as n grows.
- Simulate to confirm it.
- Change one assumption (recall allowed, a known n, ranking errors) and judge how robust the rule is.
Pitfalls
- Applying the rule to situations that break its assumptions without saying so.
- Simulating too few trials to tell strategies apart.
Where to start reading
- Algorithms to Live By (Brian Christian and Tom Griffiths)
- Search for: secretary problem 1/e proof
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