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We love music festivals. Hell, we’ll put up with just about anything to see all of our favourite bands in one day – shirtless bogans, overpriced grog, and more shirtless bogans. But we must say, the amenities offered at most festivals do make us want make like Iron Maiden and run to the hills.
Luckily, the good folks at Numberphile — a group of YouTubers who take a mathematical approach to solving everyday problems like cutting cake to playing Yahtzee — have made use of statistics and ratios to help festivalgoers find the most sanitary toilets at any festival they attend.
According to the clip’s presented, Dr Ria Symonds of the University of Nottingham, the problem at the heart of this mathematical conundrum is that “you’ve got hundreds of these toilets” so, “How do you know to know which toilet to stop on and decide to use, so you don’t have to try them all?”
“There must an optimum number we can look at,” she adds. Going into Dr Symonds’ mathematical experiment, keep in mind two crucial factors: that the best toilet is the one that’s often the cleanest, and if you pass on one toilet, you can’t go back because the line has already moved forward.
Dr Symonds then presents a model involving three toilets – Number 1 is the cleanest, Number 2 slightly messier, and Number 3 a wasteland. Of course, in real life, the toilets won’t be ordered in such a convenient fashion. There’s actually six different permutations of how the toilets might be ordered, with the chances of hitting Number 1 on the first go sinking as you add more toilets.
Your first step in securing the best toilet is then to reject the very first toilet and choose the toilet that is the “best so far.” In the case of three toilets where you immediately reject the first choice, you have a 50% chance of picking toilet Number 1. Increasing the number of toilets to four, the “reject the first, choose the best so far” method gives you a 46% chance of nabbing the cleanest toilet.
According to Dr Symonds, the percentages fall by some 4% with each new toilet you introduce to the situation, meaning this method isn’t the most effective for large-scale events as you’d have to scope out 37% of the toilets. Check the videos below for Dr Symonds’ detailed explanation.
Watch: Mathematical Way To Choose A Toilet
Watch: Choosing Toilets – Extended Ending
