Operations research Wait, what?

The Delivery Route Problem That Breaks Computers

Visiting 15 towns has absurdly many routes

Lesson notes

Key points

With n towns and a fixed start, a round trip has (n−1)! orders, halved because each loop can run in either direction.
Add just a few more towns and checking every route takes longer than any computer could finish, so OR uses smarter methods.

Takeaway: Route counts grow factorially, so brute force fails fast.

Quick check: How do route counts grow as you add towns?

Slowly, by addition
Factorially, very fast
They stay the same

Routes grow like (n−1)!/2, which explodes quickly.

Factorial growthCombinatorial explosion

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