# Combinatorics and Pampers

I’m a mom of a toddler and a newborn, so my house goes through a lot of diapers. We’ve been using Pampers almost exclusively since my son was born in 2010. Pampers offers a program called “Pampers Rewards” where you can enter codes found on Pampers products to their website, and redeem for cool stuff. (Let’s agree to ignore all issues about the effects of disposable diapers on the world ecology, or on family size and the exponentially growing population of humans on our planet, or the obvious questions about why Pampers is trading me stuff for lots of data about how often my kids pee.)

The coding scheme that Pampers uses has bothered me for a while. Each Pampers item comes with an alphanumeric 15-digit code, something like “T9PDXPKKGA3M4GK”. Given that for each character we have 36 possibilities, and the codes are 15 characters long, there are a whopping 3615 such codes. This is about 2.2×1023. That’s a lot of possible codes! How many? If every single one of the seven billion people (7×109)  on the planet used Pampers, there would be enough possible codes for each person to have one billion codes just for themselves — and then there would still be some left over. While my kids use a lot of diapers, I surely hope we don’t end up needing a billion boxes of Pampers for each of them.

Why does Pampers do this? I am not sure. Instead of an alphanumeric code, why not just use an alphabetical sequence of length 15? This would mean “only” 2615, or a little shy of 1.7×1021. In this case, there would still be more than a billion codes available for each one of the seven billion of us.

It’s in Pampers’s interest to make sure only a small percentage of all possible codes are actually connected with a particular product; this prevents fraud on their Rewards program. If I were going to design codes, I’d want to make sure that of all possible codes, maybe only one in a million actually worked. I’ll even be very cautious and allow only one in ten billion (1 in 1010) to actually appear on a product. What is one ten-billionth of 3615? It’s about 2.2×1013. This would still leave Pampers with over ten trillion (1013) usable codes. Surely they could find a more efficient coding scheme.

Apart from efficiency, I’d really love it if Pampers would just print the associated QR code along with the actual 15-digits. Having to type in multiple 15-digit codes on my Pampers iPhone app, while chasing a toddler, nursing a newborn, and typing a blog post, is really quite taxing!

## 5 thoughts on “Combinatorics and Pampers”

1. Huh, I hadn’t thought of that before. Then again, I hadn’t noticed the Pampers Rewards program either. I wonder if they use something like how credit card numbers need to pass a checksum test? There are probably hundreds of checksum-based codes out there, so ensuring that their numbers are unique among all reward codes might also be a motivation. For example, if Coke Rewards codes worked as Pampers Rewards codes, it would be a disaster for Pampers. As for the QR code idea… Well, we don’t want (a) people scanning QR codes in the supermarket and then just not buying the product or (b) too many people to take advantage of the Rewards program. Make things too easy and the expected value of a rewards code for a company will go negative!

• As far as item (a), the codes themselves are inside the packaging. There is a “Pampers Rewards” symbol on the outside of the box, but the codes themselves are stickers placed on the plastic bags that hold the diapers. So unless people are opening un-purchased boxes of diapers in retail establishments, QR tags shouldn’t be an issue.

I’ve thought about (b) too: Maybe making it this annoying cuts down on the number of consumers who participate in the rewards program? I wonder if this is it, or not. I think that Pampers execs have carefully and cautiously calculated the expense-to-benefit ratio of the rewards program itself. What they are giving me isn’t “free” since I am happily trading lots of data about my family that they can (and I’m sure do) sell to marketers. They know I have a toddler boy, that we are in the process of potty training, and that we go swimming regularly during the summers. This information has some cash value to them. Given this, wouldn’t they want more people participating, not fewer?

Really, my complaint is that entering the types of codes that they have chosen is an annoying process. Why not make it easier on me?!!

2. I like that you said,”or fewer” rather than “or less.”
I remember a time when I thought the time when our family was done with needing diapers would be a halcyon age where we had a lot less stuff in our house. How wrong I was!