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Definition Village News
6th June 2020
Interview with Max Imum and Sue Premum
Liz Windxor
It was a bright cold day in April, and the clocks were striking thirteen. The county council have repeatedly assured us that they're working on fixing the clocks, but that's another story. On this bright cold day in April, I was on my way to The George to have lunch with Max Imum and Sue Premum, top executives at the Π∋∋ Sticker Company. Over lunch, we talked at great length about mathematics, stickers, and life in Approxfordshire.

The George
Image: JThomas, CC BY-SA 2.0
What is the sticker book?
Not all Definition Village residents will be familiar with the sticker book, so I began by asking Max and Sue about how they'd explain stickers to a complete newbie.
“The sticker book,” explained Sue, “is something we started doing last year to tie in with The Big Internet Math-Off. We designed 162 stickers showing the competitors and their entries. We then sold packs of five random stickers, and collectors bought these and swapped spare stickers with friends to try to collect them all.
“This year, the sticker book is slightly different, due to the unusual tournament format. As the length of the tournament and the competitors are not known, we initially released a small sticker book, and are releasing more pages and more generations of stickers as the tournament continues.”
At the time of the interview, six generations of stickers had been released. Since then, four further generations have been released.
How to get started
Next, I asked how people who were late-comers to the sticker book could best join in.
“You'll make a pretty good start if you stay here in Definition Village,” said Max. “The Definition Village shop has lots of early generation stickers in stock, at pretty low prices now that the demand for these generations has dropped. Other collectors are being pretty generous with swapping too, especially with the early generations as most collectors no longer have any use for these swaps. Before swapping stickers with someone, you'll need to be friends. Click on the + next to people on the leaderboard to send them a friend request.
“After a while, you might like to travel around to look for different sticker packs. The bus from here to Theorem Town is quite expensive, but you'll find stickers in Theorem Town that you can't find here. When you visit a new location, you should buy the location's stickers: these are the first items in the location's shop, and will add that location to your map. In the pack, you'll get three copies of the same location sticker; you can swap two of these with friends. If you're lucky, friends will give you other location stickers to help add to your map.
“Unless you buy a prize pack with a lot of money in it, you probably can't afford to visit every location. You should use swapping to help you get stickers from locations you can't get to: buy lots of extra stickers so you have something to swap!”
Avid collectors may have noticed that they are able to swap stickers with all their friends, even those currently travelling in distant sticker-selling cities. I couldn't let Max talk about swapping without asking about how the Π∋∋ Sticker Company achieves this.
“As head of our research division,” Max said, “Sue is in the best position to explain this.”

A Klein bottle
“The swapping system,” Sue proceeded, “is powered entirely by Klein bottles. Our research division recently discovered a method of building a true Klein bottle. I don't fully understand exactly what they did, but the researchers involved ensure me that it is made possible by considering 'spin' as the fourth dimension. By placing identical Klein bottles in different locations, we are able to transport stickers almost instantly between the locations.
“Imagine that Alice is trying to send stickers to Bob. Alice starts by putting the stickers inside her Klein bottle. The stickers are now inside Alice's bottle and outside Bob's bottle. But the inside and outside of a Klein bottle are actually the same region, and so the stickers are actually outside Alice's Klein bottle and inside Bob's. Bob can now take the stickers out of his Klein bottle and they have been transported.
“This isn't the only technological advance funded by our sticker profits: many of your readers may have spent a night in one of our Π∋∋ bed and breakfast pods. These provide free places for sticker collectors to sleep across the county; very useful for those travelling far from home in search of stickers.”
Sticker exclusivity
I was bonding with Max and Sue, and lunch had just arrived at our table, so it was time to ask a more challenging question. I probed them about their recent sales of exclusive sticker rights and the hoarding of these rights by Remainder Village.
“It's a necessary evil,” said Max. “We need the money that these sales bring in to fund our research division. I agree that it would be nice if all stickers were available everywhere, but we decided it was more important to fund our sticker Klein bottles, bed and breadfast pods, and many other projects that our researchers are working on.”
I pushed them about our Remainder Village boycott, but they insisted that they could make no comment on this. Readers, I hope that you agree with me that this reveals that they support the boycott, but cannot publicly declare this while acting as spokespeople for the Π∋∋ Sticker Company.
Favourite stickers
At this point, we were close to finishing lunch, and Max and Sue had important business to get back to. I ended the interview by asking Max and Sue about their favourite stickers.

Sticker 305
Sue began: “My favourite is actually not out yet [it has now been released as part of generation 7], but has just been designed. It's going to be sticker 305.
“It's a sticker about Goldbach's conjecture, which is going to be on our page of unsolved problems.
“Goldbach's conjecture states that every even number greater than 4 can be written as the sum of two prime numbers. The sticker shows how this is done for the even numbers up to 48. I think this is a really interesting unsolved problem: it's so easy to explain what it is, and I find it really surprising that no-one has yet solved such an easy-sounding problem.”

Sticker 148
Max then revealed his favourite sticker: “I'm a big fan of geometry puzzles, so you won't be surprised to hear that I'm also a big fan of Catriona Shearer. Sticker 148 has one of her puzzles on it, and so is my favourite.
“When I pulled this sticker out of a pack that I bought in Hexagon village, I spend a good 20 minutes staring at it and attempting to solve it. I was so satisfied when I finally solved it.”
I thanked Max and Sue for their time, and they headed to the bus stop to catch a bus back to Theorem Town. I walked home, and popped into the Definition Village shop on my way home to buy some stickers.
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