One of the points where mathematics and day-to-day intuitions jar is in estimating numbers of combinations and similar combinatorial problems. I’ve just made a booking on Eurostar, and my confirmation code is a 6-letter code. Surely, my intuitive brain says, this isn’t enough; all of those people going on all of those journeys on those really long trains, day-in, day-out. Yet there are a vast number of possibilities; with one letter of the 26 letter alphabet for each of the 6 letters in the code, there are 26^6=308,915,776 possible combinations. Given that there are 10 million Eurostar passengers each year, this is enough to allocate unique codes for passengers for around thirty years. It then makes you wonder why some codes are so long, like the 90-digit MATLAB registration code that I had to type in by hand a couple of years ago.