Your favorite band is great at playing music, but not so great at being organized.
They keep misplacing their instruments on tour, and it's driving their manager mad.
On the day of the big concert, the band wakes up to find themselves tied up in a windowless, soundproof practice room.
Their manager explains what's happening.
Outside, there are ten large boxes.
Each contains one of your instruments, but don't be fooled by the pictures - they've been randomly placed.
I'm going to let you out one at a time.
While you're outside, you can look inside any five boxes before security takes you back to the tour bus.
You can't touch the instruments or in any way communicate what you find to the others.
No marking the boxes, shouting, nothing.
If each one of you can find your own instrument, then you can play tonight.
Otherwise, the label is dropping you.
You have three minutes to think about it before we start.
The band is in despair.
After all, each musician only has a 50% chance of finding their instrument by picking five random boxes.
And the chances that all ten will succeed are even lower - just 1 in 1024.
But suddenly, the drummer comes up with a valid strategy that has a better than 35% chance of working.
Can you figure out what it was?
Pause the video on the next screen if you want to figure it out for yourself!
Answer in: 3 Answer in: 2 Answer in: 1 Here's what the drummer said: Everyone first open the box with the picture of your instrument.
If your instrument is inside, you're done.
Otherwise, look at whatever's in there, and then open the box with that picture on it.
Keep going that way until you find your instrument.
The bandmates are skeptical, but amazingly enough, they all find what they need.
And a few hours later, they're playing to thousands of adoring fans.
So why did the drummer's strategy work?
Each musician follows a linked sequence that starts with the box whose outside matches their instrument and ends with the box actually containing it.
Note that if they kept going, that would lead them back to the start, so this is a loop.
For example, if the boxes are arranged like so, the singer would open the first box to find the drums, go to the eighth box to find the bass, and find her microphone in the third box, which would point back to the first.
This works much better than random guessing because by starting with the box with the picture of their instrument, each musician restricts their search to the loop that contains their instrument, and there are decent odds, about 35%, that all of the loops will be of length five or less.
How do we calculate those odds?
For the sake of simplicity, we'll demonstrate with a simplified case, four instruments and no more than two guesses allowed for each musician.
Let's start by finding the odds of failure, the chance that someone will need to open three or four boxes before they find their instrument.
There are six distinct four-box loops.
One fun way to count them is to make a square, put an instrument at each corner, and draw the diagonals.
See how many unique loops you can find, and keep in mind that these two are considered the same, they just start at different points.
These two, however, are different.
We can visualize the eight distinct three-box loops using triangles.
You'll find four possible triangles depending on which instrument you leave out, and two distinct paths on each.
So of the 24 possible combinations of boxes, there are 14 that lead to faliure, and ten that result in success.
That computational strategy works for any even number of musicians, but if you want a shortcut, it generalizes to a handy equation.
Plug in ten musicians, and we get odds of about 35%.
What if there were 1,000 musicians?
1,000,000?
As n increases, the odds approach about 30%.
Not a guarantee, but with a bit of musician's luck, it's far from hopeless.
Hi everybody, if you liked this riddle, try solving these two.
It may seem like the semicolon is struggling with an identity crisis.
It looks like a comma crossed with a period.
Maybe that's why we toss these punctuation marks around like grammatical confetti.
We're confused about how to use them properly.
In fact, it's the semicolon's half-half status that makes it useful.
It's stronger than a comma, and less final than a period.
It fills the spaces in between, and for that reason, it has some specific and important tasks.
For one, it can clarify ideas in a sentence that's already festooned with commas.
"Semicolons: At first, they may seem frightening, then, they become enlightening, finally, you'll find yourself falling for these delightful punctuation marks."
Even though the commas separate different parts of the sentence, it's easy to lose track of what belongs where.
But then the semicolon edges in to the rescue.
In list-like sentences, it can exert more force than commas do, cutting sentences into compartments and grouping items that belong together.
The semicolon breaks things up, but it also builds connections.
Another of its tasks is to link together independent clauses.
These are sentences that can stand on their own, but when connected by semicolons, look and sound better because they're related in some way.
"Semicolons were once a great mystery to me.
I had no idea where to put them."
Technically, there's nothing wrong with that.
These two sentences can stand alone.
But imagine they appeared in a long list of other sentences, all of the same length, each separated by periods.
Things would get monotonous very fast.
In that situation, semicolons bring fluidity and variation to writing by connecting related clauses.
But as beneficial as they are, semicolons don't belong just anywhere.
There are two main rules that govern their use.
Firstly, unless they're being used in lists, semicolons should only connect clauses that are related in some way.
You wouldn't use one here, for instance: "Semicolons were once a great mystery to me; I'd really like a sandwich."
Periods work best here because these are two totally different ideas.
A semicolon's job is to reunite two independent clauses that will benefit from one another's company because they refer to the same thing.
Secondly, you'll almost never find a semicolon willingly stationed before coordinating conjunctions: the words, "and," "but," "for," "nor," "or," "so," and "yet."
That's a comma's place, in fact.
But a semicolon can replace a conjunction to shorten a sentence or to give it some variety.
Ultimately, this underappreciated punctuation mark can give writing clarity, force, and style, all encompassed in one tiny dot and squiggle that's just waiting to be put in the right place.
In ancient Greece, headaches were considered powerful afflictions.
Victims prayed for relief from Asclepius, the god of medicine.
And if pain continued, a medical practitioner would perform the best-known remedy— drilling a small hole in the skull to drain supposedly infected blood.
This dire technique, called trepanation, often replaced the headache with a more permanent condition.
Fortunately, doctors today don’t resort to power tools to cure headaches.
But we still have a lot to learn about this ancient ailment.
Today, we’ve classified headaches into two camps— primary headaches and secondary headaches.
The former are not symptomatic of an underlying disease, injury, or condition; they are the condition.
But we’ll come back to them in a minute because while primary headaches account for 50% of reported cases, we actually know much more about secondary headaches.
These are caused by other health problems, with triggers ranging from dehydration and caffeine withdrawal to head and neck injury, and heart disease.
Doctors have classified over 150 diagnosable types, all with different potential causes, symptoms, and treatments.
But we’ll take just one common case —a sinus infection—as an example.
The sinuses are a system of cavities that spread behind our foreheads, noses, and upper cheeks.
When our sinuses are infected, our immune response heats up the area, roasting the bacteria and inflaming the cavities well past their usual size.
The engorged sinuses put pressure on the cranial arteries and veins, as well as muscles in the neck and head.
Their pain receptors, called nociceptors, trigger in response, cueing the brain to release a flood of neuropeptides that inflame the cranial blood vessels, swelling and heating up the head.
This discomfort, paired with hyper-sensitive head muscles, creates the sore, throbbing pain of a headache.
Not all headache pain comes from swelling.
Tense muscles and inflamed, sensitive nerves cause varying degrees of discomfort in each headache.
But all cases are reactions to some cranial irritant.
While the cause is clear in secondary headaches, the origins of primary headaches remain unknown.
Scientists are still investigating potential triggers for the three types of primary headaches: recurring, long-lasting migraines; intensely painful, rapid-fire cluster headaches; and, most common of all, the tension headache.
As the name suggests, tension headaches are known for creating the sensation of a tight band squeezed around the head.
These headaches increase the tenderness of the pericranial muscles, which then painfully pulse with blood and oxygen.
Patients report stress, dehydration, and hormone changes as triggers, but these don’t fit the symptoms quite right.
For example, in dehydration headaches, the frontal lobe actually shrinks away from the skull, creating forehead swelling that doesn’t match the location of the pain in tension headaches.
Scientists have theories for what the actual cause is, ranging from spasming blood vessels to overly sensitive nociceptors, but no one knows for sure.
Meanwhile, most headache research is focused on more severe primary headaches.
Migraines are recurring headaches, which create a vise-like sensation on the skull that can last from four hours to three days.
In 20% of cases, these attacks are intense enough to overload the brain with electrical energy, which hyper-excites sensory nerve endings.
This produces hallucinations called auras, which can include seeing flashing lights and geometric patterns and experiencing tingling sensations.
Cluster headaches, another primary headache type, cause burning, stabbing bursts of pain behind one eye, leading to a red eye, constricted pupil, and drooping eyelid.
What can be done about these conditions, which dramatically affect many people’s quality of life?
Tension headaches and most secondary cases can be treated with over-the-counter pain medications, such as anti-inflammatory drugs that reduce cranial swelling.
And many secondary headache triggers, like dehydration, eye strain, and stress, can be proactively avoided.
Migraines and cluster headaches are more complicated, and we haven’t yet discovered reliable treatments that work for everyone.
But thankfully, pharmacologists and neurologists are hard at work cracking these pressing mysteries that weigh so heavily on our minds.
When I wrote my memoir, the publishers were really confused.
Was it about me as a child refugee, or as a woman who set up a high-tech software company back in the 1960s, one that went public and eventually employed over 8,500 people?
Or was it as a mother of an autistic child?
Or as a philanthropist that's now given away serious money?
Well, it turns out, I'm all of these.
So let me tell you my story.
All that I am stems from when I got onto a train in Vienna, part of the Kindertransport that saved nearly 10,000 Jewish children from Nazi Europe.
I was five years old, clutching the hand of my nine-year-old sister and had very little idea as to what was going on.
"What is England and why am I going there?"
I'm only alive because so long ago, I was helped by generous strangers.
I was lucky, and doubly lucky to be later reunited with my birth parents.
But, sadly, I never bonded with them again.
But I've done more in the seven decades since that miserable day when my mother put me on the train than I would ever have dreamed possible.
And I love England, my adopted country, with a passion that perhaps only someone who has lost their human rights can feel.
I decided to make mine a life that was worth saving.
And then, I just got on with it.
(Laughter) Let me take you back to the early 1960s.
To get past the gender issues of the time, I set up my own software house at one of the first such startups in Britain.
But it was also a company of women, a company for women, an early social business.
And people laughed at the very idea because software, at that time, was given away free with hardware.
Nobody would buy software, certainly not from a woman.
Although women were then coming out of the universities with decent degrees, there was a glass ceiling to our progress.
And I'd hit that glass ceiling too often, and I wanted opportunities for women.
I recruited professionally qualified women who'd left the industry on marriage, or when their first child was expected and structured them into a home-working organization.
We pioneered the concept of women going back into the workforce after a career break.
We pioneered all sorts of new, flexible work methods: job shares, profit-sharing, and eventually, co-ownership when I took a quarter of the company into the hands of the staff at no cost to anyone but me.
For years, I was the first woman this, or the only woman that.
And in those days, I couldn't work on the stock exchange, I couldn't drive a bus or fly an airplane.
Indeed, I couldn't open a bank account without my husband's permission.
My generation of women fought the battles for the right to work and the right for equal pay.
Nobody really expected much from people at work or in society because all the expectations then were about home and family responsibilities.
And I couldn't really face that, so I started to challenge the conventions of the time, even to the extent of changing my name from "Stephanie" to "Steve" in my business development letters, so as to get through the door before anyone realized that he was a she.
(Laughter) My company, called Freelance Programmers, and that's precisely what it was, couldn't have started smaller: on the dining room table, and financed by the equivalent of 100 dollars in today's terms, and financed by my labor and by borrowing against the house.
My interests were scientific, the market was commercial -- things such as payroll, which I found rather boring.
So I had to compromise with operational research work, which had the intellectual challenge that interested me and the commercial value that was valued by the clients: things like scheduling freight trains, time-tabling buses, stock control, lots and lots of stock control.
And eventually, the work came in.
We disguised the domestic and part-time nature of the staff by offering fixed prices, one of the very first to do so.
And who would have guessed that the programming of the black box flight recorder of Supersonic Concord would have been done by a bunch of women working in their own homes.
(Applause) All we used was a simple "trust the staff" approach and a simple telephone.
We even used to ask job applicants, "Do you have access to a telephone?"
An early project was to develop software standards on management control protocols.
And software was and still is a maddeningly hard-to-control activity, so that was enormously valuable.
We used the standards ourselves, we were even paid to update them over the years, and eventually, they were adopted by NATO.
Our programmers -- remember, only women, including gay and transgender -- worked with pencil and paper to develop flowcharts defining each task to be done.
And they then wrote code, usually machine code, sometimes binary code, which was then sent by mail to a data center to be punched onto paper tape or card and then re-punched, in order to verify it.
All this, before it ever got near a computer.
That was programming in the early 1960s.
In 1975, 13 years from startup, equal opportunity legislation came in in Britain and that made it illegal to have our pro-female policies.
And as an example of unintended consequences, my female company had to let the men in.
(Laughter) When I started my company of women, the men said, "How interesting, because it only works because it's small."
And later, as it became sizable, they accepted, "Yes, it is sizable now, but of no strategic interest."
And later, when it was a company valued at over three billion dollars, and I'd made 70 of the staff into millionaires, they sort of said, "Well done, Steve!"
(Laughter) (Applause) You can always tell ambitious women by the shape of our heads: They're flat on top for being patted patronizingly.
(Laughter) (Applause) And we have larger feet to stand away from the kitchen sink.
(Laughter) Let me share with you two secrets of success: Surround yourself with first-class people and people that you like; and choose your partner very, very carefully.
Because the other day when I said, "My husband's an angel," a woman complained -- "You're lucky," she said, "mine's still alive."
(Laughter) If success were easy, we'd all be millionaires.
But in my case, it came in the midst of family trauma and indeed, crisis.
Our late son, Giles, was an only child, a beautiful, contented baby.
And then, at two and a half, like a changeling in a fairy story, he lost the little speech that he had and turned into a wild, unmanageable toddler.
Not the terrible twos; he was profoundly autistic and he never spoke again.
Giles was the first resident in the first house of the first charity that I set up to pioneer services for autism.
And then there's been a groundbreaking Prior's Court school for pupils with autism and a medical research charity, again, all for autism.
Because whenever I found a gap in services, I tried to help.
I like doing new things and making new things happen.
And I've just started a three-year think tank for autism.
And so that some of my wealth does go back to the industry from which it stems, I've also founded the Oxford Internet Institute and other IT ventures.
The Oxford Internet Institute focuses not on the technology, but on the social, economic, legal and ethical issues of the Internet.
Giles died unexpectedly 17 years ago now.
And I have learned to live without him, and I have learned to live without his need of me.
Philanthropy is all that I do now.
I need never worry about getting lost because several charities would quickly come and find me.
(Laughter) It's one thing to have an idea for an enterprise, but as many people in this room will know, making it happen is a very difficult thing and it demands extraordinary energy, self-belief and determination, the courage to risk family and home, and a 24/7 commitment that borders on the obsessive.
So it's just as well that I'm a workaholic.
I believe in the beauty of work when we do it properly and in humility.
Work is not just something I do when I'd rather be doing something else.
We live our lives forward.
So what has all that taught me?
I learned that tomorrow's never going to be like today, and certainly nothing like yesterday.
And that made me able to cope with change, indeed, eventually to welcome change, though I'm told I'm still very difficult.
Thank you very much.
(Applause)