A family member recently sent me a puzzle:
One hundred people are lined up with their boarding passes showing their seats on the 100-seat Plane. The first guy in line drops his pass as he enters the plane, and unable to pick it up with others behind him sits in a random seat. The people behind him, who have their passes, sit in their seats until one of them comes upon someone sitting in his seat, and takes his seat in a new randomly chosen seat. This process continues until there is only one seat left for the last person.
What is the probability that the last person will sit in the correct seat?
This took me a little time to work out mathematically (if you want some good solutions and explanations, see here). But I became interested in solving the problem using a Monte Carlo simulation.
R is excellent at solving many kinds of probability puzzles through simulation, often with concise and efficient approaches. For a puzzle like “What are the chances three people on an elevator with 13 buttons press three consecutive floors”, an R simulation can easily fit in a tweet:
mean(replicate(1e5, all(diff(sort(sample(13, 3, TRUE))) == 1)))## [1] 0.02951But it’s not immediately obvious how to simulate the boarding pass puzzle in R. This is because there’s a relationship between each passenger’s options and the choices of previous passengers. This means we have to keep track of state across steps, which makes it difficult to use our usual vectorization tricks. If we’re not careful, we might start building loops within loops and building up objects incrementally, approaches which are very slow in R.
Here I’ll show how to approach a puzzle like this while still taking advantage of R vectorization. Though I’ll walk through the code, this …read more
Source:: r-bloggers.com