Of Patterns, Probabilities and Palindromes
We discovered an interesting little problem last week. Interesting, that is, if you enjoy Maths a little more than is healthy. I was interested because what seemed to be a random problem when it should have been consistent, turned out just to be a random problem.
So here is what was happening. Our Sitewatcher was randomly showing a few sites returning 404 (page not found) errors. This was curious, because it was requesting the home page, and this page was certainly not missing. As it happens, there is a tiny weeny glitch with a couple of sites in that they will return a 404 code on the home page if the number 404 features in the query-string. This doesn’t happen in normal circumstances, but as cache:false was being used with jQuery, it was appending a random number to the request.
So here is the question. What is the probability of the number 404 occurring in a random 10 digit sequence? Not so trivial. Particularly because the number is itself is a palindrome. It can overlap itself, causing the number to appear as often as 4 times, making the calculation a little tricky.
We reckoned, by rough estimations, for it to be 1 in ~125, but no doubt a serious mathematician can enlighten us.
Tags: maths, probability, programming, websites
