Dutch artist Piet Mondrian’s abstract, rectangular paintings inspired mathematicians to create a two-fold challenge.
First, we must completely cover a square canvas with non-overlapping rectangles.
All must be unique, so if we use a 1x4, we can’t use a 4x1 in another spot, but a 2x2 rectangle would be fine.
Let’s try that.
Say we have a canvas measuring 4x4.
We can’t chop it directly in half, since that would give us identical rectangles of 2x4.
But the next closest option - 3x4 and 1x4 - works.
That was easy, but we’re not done yet.
Now take the area of the largest rectangle, and subtract the area of the smallest.
The result is our score, and the goal is to get as low a score as possible.
Here, the largest area is 12 and the smallest is 4, giving us a score of 8.
Since we didn’t try to go for a low score that time, we can probably do better.
Let’s keep our 1x4 while breaking the 3x4 into a 3x3 and a 3x1.
Now our score is 9 minus 3, or 6.
Still not optimal, but better.
With such a small canvas, there are only a few options.
But let’s see what happens when the canvas gets bigger.
Try out an 8x8; what’s the lowest score you can get?
Pause here if you want to figure it out yourself.
Answer in: 3 Answer in: 2 Answer in: 1 To get our bearings, we can start as before: dividing the canvas roughly in two.
That gives us a 5x8 rectangle with area 40 and a 3x8 with area 24, for a score of 16.
That’s pretty bad.
Dividing that 5x8 into a 5x5 and a 5x3 leaves us with a score of 10.
Better, but still not great.
We could just keep dividing the biggest rectangle.
But that would leave us with increasingly tiny rectangles, which would increase the range between the largest and smallest.
What we really want is for all our rectangles to fall within a small range of area values.
And since the total area of the canvas is 64, the areas need to add up to that.
Let’s make a list of possible rectangles and areas.
To improve on our previous score, we can try to pick a range of values spanning 9 or less and adding up to 64.
You’ll notice that some values are left out because rectangles like 1x13 or 2x9 won’t fit on the canvas.
You might also realize that if you use one of the rectangles with an odd area like 5, 9, or 15, you need to use another odd-value rectangle to get an even sum.
With all that in mind, let’s see what works.
Starting with area 20 or more puts us over the limit too quickly.
But we can get to 64 using rectangles in the 14-18 range, leaving out 15.
Unfortunately, there’s no way to make them fit.
Using the 2x7 leaves a gap that can only be filled by a rectangle with a width of 1.
Going lower, the next range that works is 8 to 14, leaving out the 3x3 square.
This time, the pieces fit.
That’s a score of 6.
Can we do even better?
No.
We can get the same score by throwing out the 2x7 and 1x8 and replacing them with a 3x3, 1x7, and 1x6.
But if we go any lower down the list, the numbers become so small that we’d need a wider range of sizes to cover the canvas, which would increase the score.
There’s no trick or formula here – just a bit of intuition.
It's more art than science.
And for larger grids, expert mathematicians aren’t sure whether they’ve found the lowest possible scores.
So how would you divide a 4x4, 10x10, or 32x32 canvas?
Give it a try and post your results in the comments.
This is the Air Jordan 3 Black Cement.
This might be the most important sneaker in history.
First released in 1988, this is the shoe that started Nike marketing as we know it.
This is the shoe that propelled the entire Air Jordan lineage, and perhaps saved Nike.
The Air Jordan 3 Black Cement did for sneakers what the iPhone did for phones.
It's been re-released four times.
Every celebrity's been seen wearing it.
There's a site about what to wear with the Black Cement.
It's been right under your nose for decades and you never looked down.
And right about now, most of you are probably thinking, "Sneakers?"
(Laughter) Yes.
Yes, sneakers.
Some extraordinary things about sneakers and data and Nike and how they're all related, possibly, to the future of all online commerce.
In 2011, the last time the Jordan 3 Black Cement was released, at a retail of 160 dollars, it sold out globally in minutes.
And that's because people were camped outside of sneaker stores for days before it went on sale.
And just minutes after that, thousands of those pairs were on eBay for two and three times retail.
In fact, there's over 1,000 pairs on eBay right now, four years later.
But here's the thing: this happens every single Saturday.
Every week there's another release or two or three, and every shoe has a story as rich and compelling as the Jordan 3 Black Cement.
This is Nike building the marketplace for sneakerheads -- people who collect sneakers -- and my daughter.
(Laughter) That's an "I love Dad" T-shirt.
For the brands, sneakerheads are a very important demographic.
These are the tastemakers; these are the Apple fanboys.
Because who else is going to buy a pair of $8,000 Back to the Future sneakers?
(Laughter) Yeah, 8,000 dollars.
And while that's obviously the anomaly, the resell sneaker market is definitely not.
Thirty years in the making, what started as an underground culture of a few people who like sneakers just a bit too much -- (Laughter) Now we have sneaker addictions.
In a market where in the past 12 months, there have been over nine million pairs of shoes resold in the United States alone, at a value of 1.2 billion dollars.
And that's a conservative estimate -- I should know, I am a sneakerhead.
This is my collection.
In the pantheon of great collections, mine doesn't even register.
I have about 250 pairs, but trust me, I am small-time.
People have thousands.
I'm a very typical 37-year-old sneakerhead.
I grew up playing basketball when Michael Jordan played, I always wanted Air Jordans, my mother would never buy me Air Jordans, as soon as I got some money I bought Air Jordans -- literally, we all have the exact same story.
But here's where mine diverged.
After starting three companies, I took a job as a strategy consultant, when I very quickly realized that I didn't know the first thing about data.
But I learned, because I had to, and I liked it.
So I thought, I wonder if I could get ahold of some sneaker data, just to play with for my own amusement.
The goal was to develop a price guide, a real data-driven view of the market.
And four years later, we're analyzing over 25 million transactions, providing real-time analytics on thousands of sneakers.
Now sneakerheads check prices while camping out for releases.
Others have used the data to validate insurance claims.
And the top investment banks in the world now use resell data to analyze the retail footwear industry.
And here's the best part: sneakerheads have sneaker portfolios.
(Laughter) Sneakerheads can track the value of their collection over time, compare it to others, and have access to the same analytics you might for your online brokerage account.
So sneakerhead Dan builds his collection and identifies which 352 are his.
He can see it's worth 103,000 dollars -- frankly, a modest collection.
At the asset level, he can see gain-loss by shoe.
Here he's made over 600 dollars on one pair.
I have one of those.
(Laughter) So an unregulated 1.2 billion dollar industry that thrives as much on the street as it does online, and has spawned fundamental financial services for sneakers?
At some point I asked myself what's really going on in the market, and two comparisons started to emerge.
Are sneakers more like stocks or drugs?
(Laughter) In fact, one guy emailed to say he thought his 15-year-old son was selling drugs and later found out he was selling sneakers.
(Laughter) And now they use the data to do it together.
And that's because sneakers are an investment opportunity where none other exists.
And I don't just mean the kid selling sneakers instead of drugs.
How about all kids?
You have to be 18 to play the stock market.
I sold chewing gum in sixth grade, Blow Pops in ninth grade and collected baseball cards through high school.
The cards are long dead, and the candy market's usually quite local.
For a lot of people, sneakers are a legal and accessible investment opportunity -- a democratized stock market, but also unregulated.
Which is why the story you're probably most familiar with is people killing each other for sneakers.
And while that definitely happens and is tragic, it's not nearly the epidemic some media would have you believe.
In fact, it's a very small piece of a much bigger and better story.
So sneakers have clear similarities to both the stock exchange and the illegal drug trade, but perhaps the most fundamental is the existence of a central actor.
Someone is making the rules.
In the case of sneakers, that someone is Nike.
Let me walk you through some numbers.
The resell market, we know, is $1.2 billion.
Nike, including Jordan brand, accounts for 96 percent of all shoes sold on the secondary market.
Just complete domination.
Sneakerheads love Jordans.
And profit on the secondary market is about a third.
That means that sneakerheads made 380 million dollars selling Nikes last year.
Let's jump to retail for a second.
Skechers, earlier this year, became the number two footwear brand in the country, surpassing Adidas -- this was a big deal.
And in the 12 months ending in June, Skechers's net income was 209 million dollars.
That means that Nike's customers make almost twice as much profit as their closest competitor.
That -- (Laughter) How is that even possible?
The sneaker market is just supply and demand, but Nike's gotten very good at using supply -- limited sneakers -- and the distribution of those sneakers to their own benefit.
So it's really just supply.
Sneakerheads joke that as long as it's limited and Nike, they'll buy it.
Shoes that sell for 8,000 dollars do so because they're very rare.
It's no different than any other collectible market, only this isn't a bensonnicole@example.net.
It's a false construct created by Nike -- ingeniously created by Nike, in the most positive sense -- to sell more shoes.
And in the process, it provided tens of thousands of people with life-long passions, myself included.
If Nike wanted to kill the resell market, they could do so tomorrow, all they have to do is release more shoes.
But we certainly don't want them to, nor is it in their best interest.
That's because unlike Apple, who will sell an iPhone to anyone who wants one, Nike doesn't make their money by just selling $200 sneakers.
They sell millions of shoes to millions of people for 60 dollars.
And sneakerheads are the ones who drive the marketing and the hype and the PR and the brand cachet, and enable Nike to sell millions of $60 sneakers.
It's marketing.
It's marketing the likes of which has never been seen before -- this isn't in any textbook.
For 15 years Nike has propped up an artificial commodities market, with a Facebook-level hyped IPO every single weekend.
Drive by any Footlocker at 8am on a Saturday morning, and there will be a line down the street and around the block, and sometimes those kids have been waiting there all week.
You know those crazy iPhone lines you see on the news every other year?
Nike lines happen 104 times more often.
So Nike sets the rules.
And they do so by controlling supply and distribution.
But once a pair leaves the retail channel, it's the Wild West.
There are very few -- if any -- legal, unregulated markets of this size.
So Nike is definitely not the stock exchange.
In fact, there is no central exchange.
By last count, there were 48 different online markets that I know of.
Some are eBay clones, some are mobile markets, and then you have consignment shops and brick-and-mortar stores, and sneaker conventions, and reseller sites, and Facebook and Instagram and Twitter -- literally, anywhere sneakerheads come into contact with each other, shoes will be bought and sold.
But that means no efficiencies, no transparency, sometimes not even authenticity.
Can you imagine if that's how stocks were bought?
What if the way to buy a share of Apple stock was to search over 100 places online and off, including every time you walk down the street just hoping to pass someone wearing some Apple stock?
Never knowing who had the best price, or even if the stock you were looking at was real.
That would surely make you say: [WTF?]
Of course that's not how we buy stock.
But what if that's not how we need to buy sneakers either?
What if the inverse is true, and what if we could buy sneakers exactly the same way as we buy stock?
And what if it wasn't just sneakers, but any similar product, like watches and handbags and women's shoes, and any collectible, any seasonal item and any markdown item?
What if there was a stock market for commerce?
A stock market of things.
And not only could you buy in a much more educated and efficient manner, but you could engage in all the sophisticated financial transactions you can with the stock market.
Shorts and options and futures and well, maybe you see where this is going.
Maybe you want to invest in a stock market of things.
Because if you had invested in a pair of Air Jordan 3 Black Cement in 2011, you could either be wearing them onstage, (Laughter) or have earned 162 percent on your money -- double the S&amp;P and 20 percent more than Apple.
(Laughter) And that's why we're talking about sneakers.
Thank you.
(Applause)