Blog 53: Pigeonhole Principle by Xavier Lo, FIA, FRM, MBA

I keep saying that the perfect actuary is one who is great with numbers, but even better in soft skills and overall knowledge. However, its always good to remind ourselves of the theoretical concepts [理論] in mathematics, and I’ll introduce a relatively easy topic today: the Pigeonhole Principle [鴿巢原理].

If you’ve done theoretical mathematics at university [大學], you’ll probably have come across this principle. As a quick recap, the Pigeonhole Principle simply states that say you’ve got a number of items and you try to fit them into a number of boxes. If the items outnumber the boxes, then you’ll definitely have at least one box which contains more than one item. Try to imagine this in real life. Its pretty simple right? I mean its one of the more intuitive mathematical theorems [數學定理] which you can explain very easily to even perhaps a primary school student.

The more interesting question is: how do we use this in real life? Well, to give you some examples, my blog has more than 366 followers – this means I can be sure that two of my followers share the same birthday [同一個生日]. Another example may be that (in the spirit of working from home[在家工作]) your office has only 99 desks, but has 100 employees. This means that there will definitely be someone who won’t get a seat if everyone turns up to work on any given day. Or a more relevant application is if your company has sold 100 policies [保單], but you see 101 claims loss records [賠償單], you can be sure that at least one of the policies has had filed for more than 1 compensation claim.

Honestly, I don’t expect you to be able to apply this principle on a daily basis. However, what is important is that we have to remember actuaries are known to be very good at core mathematical concepts. I think that a lot of younger actuaries have become complacent in theoretical mathematics. Lets try to bring back our love for learning – even if it means having to learn the “boring” symbols and equations!