I recently had the chance to ride the Leap-the-Dips at Lakemont Park (Altoona, Pennsylvania), the world’s oldest operating roller coaster. The statistics of this 1902-vintage roller coaster might not sound impressive, as it has a maximum height of about forty feet and a greatest drop of about nine feet, but it gets rather more exciting when you consider that the roller coaster car hasn’t got any seat belts or lap bar or other restraints (just a bar you can grab onto if you so choose), and that the ride was built before the invention of upstop wheels, the wheels that actually go underneath the track and keep roller coaster cars from jumping off. At each of the dips, yes, the car does jump up and off the track, and the car just keeps accelerating the whole ride. (Side boards ensure that once the car jumps off the tracks it falls back into place.) It’s worth the visit.

Looking at the wonderful mesh of wood that makes up a classic roller coaster like this inspired the question: could any of it be original? What’s the chance that any board in it has lasted the hundred-plus years of the roller coaster’s life (including a twelve-year stretch when the ride was not running, a state which usually means routine maintenance is being skipped and which just destroys amusement park rides)? Taking some reasonable guesses about the replacement rate per year, and a quite unreasonable guess about replacement procedure, I worked out my guess, given in the subject line above, and I figure to come back and explain where that all came from.

## 5 thoughts on “Just Answer 1/e Whenever Anyone Asks This Kind Of Question”

1. I’m delighted that this could manage to be the source of one of your math puzzles just as I use it for one of my philosophy puzzles for class.

• Yeah, I’m glad it offers meaningful problems in both our fields.