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00:30Thank you very much. Good evening. Hello and welcome to Think of a Number. Or in this case, it's Think of Two Numbers. In my hands, I've got two coins and they add together to make 12p. But one is not a 10p and one is not a 2p. So what are they? They are a 10p and a 2p. One is not a 10p but the other one is. And one's not a 2p but the other one is.
00:54So 2p or not 2p? That's the answer. And the questions we'll be asking this week are all about money, money, money, money, money, money, money.
01:05For instance, we'll be asking questions like, how can you gamble and lose every time? What's so dicey about dice? How can you have a number of just three figures that's over a thousand miles long? And who has all the gold in the world? Don't look at me because I haven't got any.
01:23Right. First of all, would anybody like to gamble on the toss of a coin? Anybody? Anybody got any pocket money they want to gamble? All right. So who would like to gamble that would come down heads?
01:34Quite a lot. Who would gamble that would come down tails? Who would gamble that would come down on its edge? One. You and me against the rest. You can all have heads and tails. I'll gamble that would come down on its edge. All right.
01:51And we'll bet, I mean because you're bound to win, aren't you? So we'll bet all your pocket money? All right. And I won't spin it up because I could cheat. I could catch it between my fingers.
02:01What I'll do, I'll drop it on this table. Ready? Heads or tails, you win. On its edge. And I win.
02:12Oh! And I've won. Don't worry. Pay me later.
02:19You see, the trouble with gambling is it's a gamble. And I think the government should know that because they've got all our money.
02:27It doesn't matter which party's in power, they have to make the decisions involving billions of pounds.
02:32And they can never always be certain that the decisions they're making are absolutely right.
02:38They're the biggest gamblers of all. It's no wonder some people think they could do the job better.
02:44There now follows a partly idiotic broadcast on behalf of the nutty party.
02:48You're on!
02:50Oh, good evening. I mean, good morning. Oh, good heavens.
02:54My name's Slightly, Nigel Slightly, and I represent the NUTTY, our national union of typical Twitch and yo-yos.
03:01Yes. I don't usually do this. I usually make bicycle wheels.
03:05You see, that's why they made me their spokesman.
03:08Sort of a joke to get things started.
03:11Never mind. A bit tired.
03:12Wheel get on.
03:13You see, we at the NUTTY are fed up with the way this government keeps ruining the country.
03:20And what we say is, let us ruin the country.
03:22You see, we at the NUTTY don't know the meaning of defeat or confusion or giggle sprocket or any long words.
03:29What we do know is...
03:30What we do know is that we're fed up, absolutely fed up, with the government making the same mistakes all the time.
03:37What we say is, put us in power, and we'll make different mistakes.
03:40All the time.
03:41Take unemployment. Take earnings. Take the dog for a walk. No, no.
03:46Take taxes. We aim to lower taxes. How?
03:48Well, by letting the tyres down, so people can't go in taxes, and they'll have to get on the bus.
03:53This graph shows the things we are worried about.
03:55This shows the number of children dropping out of schools, mainly due to faulty flaws.
03:59This shows the number of people wanted by the police.
04:02If the police had looked behind letterboxes, they might find a few of them.
04:04And this shows the number of people who were injured by children dropping out of school through faulty flaws.
04:10You see, the question today is, what is the answer?
04:13No, that's the answer, isn't it?
04:15Yes.
04:15What's the question? That's the question.
04:16Yes, the question today is, what's the question?
04:19And the answer is...
04:20Could you repeat the question?
04:21No, what we of the NUTTY would do is put toll gates at each end of the M1.
04:27Have you thought of that?
04:28Oh, no.
04:28You see, the revenue from the toll gates would pay for the upkeep of toll gates at each end of the M1.
04:34Yes.
04:35So, next time you vote, folks, vote for us, folks.
04:37The NUTTY, or never use turquoise tights in Yarmouth.
04:41No, that's wrong.
04:42No, the National Union of Typical Twits and Yo-Yos.
04:44That's us.
04:45And remember that 99% of the population is nearly everybody.
04:51The fact is, politicians do have terribly difficult problems trying to invest all our money.
05:05I mean, take a billion pounds.
05:07What would you do if you had a billion pounds?
05:09Spend it.
05:11Spend it.
05:12Have you ever thought how big a billion is?
05:15A billion used to be a million times a million, but now we use the American system where a billion is a thousand times a million.
05:20But it's still a very big number.
05:22If you borrowed a billion pounds and you paid it back at a pound every second, day and night, it would take 31 years to pay it back.
05:32And if you had a billion pound notes in a pile, how high do you think the pile would be?
05:43Miles.
05:44A billion pound notes stacked in one pile would stretch 78.9 miles into the sky.
05:52Bit of a problem if you wanted the top one.
05:54Now, some people have a job of actually working with incredibly large numbers, but they use a system of shorthand.
06:03Now, does anybody know the biggest number you can write with three figures?
06:09999.
06:10999.
06:11999, you get three policemen.
06:13Yes.
06:13Have you ever seen this system?
06:22Two with a smaller two up there.
06:24Now, that means two squared.
06:27Two to the power of two.
06:28Several ways of saying it.
06:30And it means two written down two times.
06:33Two and a two multiply together.
06:35Two twos are four.
06:37So, if you get two to the power of three, it means two written down three times.
06:42Two times two times two, which is eight.
06:46If you got two to the power of four, it would mean two written down four times and all multiplied.
06:52Two twos are four.
06:52Two fours are eight.
06:53Two eights are?
06:55Sixteen.
06:56Right.
06:56Now, if you got nine to the power of nine, that would be nine written down nine times and
07:02they're all multiplied together.
07:03And the answer would be 387,420,489.
07:11But, if you wrote nine to the power of nine to the power of nine, it would be the same as
07:19writing nine to the power of 387,420,489.
07:24Which is the same as saying nine written down all that many times and every one of them multiplied
07:31together.
07:32And the answer to that sum would be a number that if you wrote it on a slip of paper with
07:39five figures to the inch, the slip of paper would be 1167 miles long, which is as far
07:46as from London to the very top of Scotland and all the way back again.
07:49All that from just three nines, which is a pretty fair number.
07:55So, let's have some fun at the fair.
07:58Have you got me money?
08:00Big money here.
08:01And I'm going to see how far it'll go.
08:03Oh, I've rolled it, but it's a loser, because this is a giant roller penny, strictly for squares.
08:13Now, this side first.
08:15Roll one disc and try and get it up.
08:16Now, this side, one disc each.
08:27Roll now.
08:31Get back in.
08:32That's it.
08:33Oh, there's one over there.
08:34This side, your other discs.
08:37Now.
08:42This side, your other discs.
08:44Now.
08:47Nearly had me leg off.
08:49Now, let's see how many winners we've got.
08:51One.
08:56Two.
08:58Nope.
08:59Nope.
09:00Nope.
09:01Nope.
09:02Nope.
09:03Nope.
09:05Nope.
09:06That's a loser.
09:09What do you think of that one?
09:10Yes.
09:11Oh, right.
09:12It's a winner.
09:13And this one's a winner.
09:14Yeah.
09:15Just four out of 40 discs.
09:19You'd have thought there'd be more winners than that.
09:21Or would you?
09:22Everybody come and get the discs back.
09:23Let's clear up.
09:28Just grab two.
09:29Any two.
09:37It's worked out right.
09:38What I've got here is a model of any one of these squares.
09:41Could be any one.
09:42We'll put it here.
09:43There you are.
09:44Now.
09:45And I've got a disc the same size as the disc that they were using.
09:48And in the middle, there's a hole.
09:50Now.
09:51If I run it around this tray, I draw a square.
09:58Now.
09:59For this disc to be in a winning position, the centre has to be in any of these positions on this line.
10:12There you are.
10:13Because if the centre of the disc is anywhere else, it's a losing throw.
10:17You see?
10:18When you look at it, you see one, two, three, four, five, six, seven, eight, nine squares.
10:26And of the nine squares, there's only one square that's got winning positions in it.
10:32So the chances of winning are only one in nine.
10:37So it's no wonder people don't win a fortune when they go to the fair.
10:40But you don't go to the fair to win a fortune.
10:42You go to the fair to enjoy yourself.
10:44And if you do go to make money, well, it's a pretty dicey thing to do.
10:48Talked about dice.
10:49Here's our dice.
10:50Here it comes.
10:50Look out.
10:51A big dice to do some rolling with.
10:57But first of all, I need somebody to mark the board.
10:59Who'd like to mark the board?
11:01You.
11:01OK.
11:02Right here.
11:03Now, there's a pen.
11:05And mark some numbers down here.
11:07Do your working down here.
11:08I'll tell you what to write in a minute.
11:10Because now I need a blindfold.
11:12Oh, you've got my blindfold.
11:14Put that on.
11:15Well, I'm doing this trick.
11:17Blindfold.
11:17Without the aid of a net.
11:20Right.
11:20Now, August, while you're here, you come and help me find the dice.
11:24Oh.
11:26Found it without you, thank you.
11:27Right.
11:28I'm going to roll the dice.
11:30I think I'll roll it this way.
11:31Is this the audience way?
11:32Yeah.
11:32Thought so.
11:33Ready?
11:33Go!
11:36Oh!
11:38It's gone back.
11:40Right.
11:40Marker, can you see the top number?
11:42Yes.
11:43Right.
11:43Put that in block A.
11:46You done it?
11:47Yeah.
11:48Tell me each time you've done it.
11:49Now, multiply by two.
11:51And add five.
11:57Stick on quiet.
12:01Right.
12:01Now, multiply that number by five.
12:06You're still there, aren't you?
12:08Yeah.
12:08You could all have gone home.
12:09All of you.
12:10OK, you've done that.
12:11Right, let's have another throw of the dice.
12:12Where's the dice?
12:13I've got it.
12:14I've got it.
12:14I've got it.
12:14Where's the audience?
12:15Up here.
12:17Here we go.
12:18Ready?
12:18Go!
12:19Look out!
12:20Where's it gone?
12:23Where's it gone?
12:23Over here.
12:24Marker, can you see the top surface?
12:26Yeah.
12:27Lovely.
12:28Put that in block B.
12:30OK.
12:30I don't need it yet.
12:31You've done that.
12:32Yeah.
12:33And add that to the previous total.
12:41Have you done that?
12:42Yes.
12:42Lovely.
12:42Now, multiply that number by ten.
12:44All you do is add a nought.
12:45As quick as that.
12:46And where's the dice?
12:47Over here.
12:49OK.
12:50I'm going to roll it again.
12:52Are you ready?
12:52Yes!
12:53Go!
12:57Where's it gone?
12:58Where's it gone?
13:00Marker, can you see the top surface?
13:02Yeah.
13:02Put that in block C.
13:05And add that to the total.
13:08The previous total.
13:13Yeah.
13:14Right.
13:15And tell me the number you've got.
13:17895.
13:178, 9, 5.
13:19And the three throws of the dice must have been 6, 4, 5.
13:25Yeah.
13:25Yeah.
13:33That's very good working out, isn't it?
13:35Now, you see how the trick works?
13:37Now, the secret in making the trick works, making the trick work, is when you get the total,
13:42still in your blindfold, you have to take away 250.
13:50And the answer is 6, 4, 5, which is the numbers of the throws on the dice.
13:58So, there we are.
14:01Now, have a look at this.
14:09An illuminated die.
14:11The history of dice goes back thousands of years, and a great folklore has grown up around them.
14:19For instance, some people think that the dice is its own calendar.
14:24For instance, each face has 4 edges, which could correspond to the 4 seasons.
14:31The dice itself has 12 edges, which could correspond to the 12 months of the year.
14:36The opposite faces of the dice add to 7, which equals the number of days in the week.
14:44Now, there are three pairs of opposite faces.
14:48Three sevens are 21, plus 3 for the three pairs is 24, the number of hours in the day.
14:54Similarly, taking the three sevens, 7 times 7 times 7 is 343, plus 7 plus 7 plus 7 is 364,
15:04which divided by 7 equals 52, the number of weeks in the year.
15:10Or, 364 plus 1 for the dice itself equals 365, the number of days in the year.
15:19And now, from a cube to a diamond.
15:35Diamonds are formed by molten rock cooling,
15:40and the intense pressure and heat forms the hardest of all crystals, diamonds.
15:45And this is a model of the largest diamond that has ever been discovered.
15:51It was found in 1905 in South Africa and called the Cullinan diamond.
15:57And it was given to King Edward VII on his 66th birthday.
16:05In 1908, the rough diamond was sent to Amsterdam to be cut by a master diamond cutter called Jacob Asher.
16:12It's very difficult to cut a diamond.
16:15If you don't hit it in absolutely the right place,
16:18you could be standing up to your knees in diamond dust.
16:22Asher carefully surveyed the stone,
16:25then set the blade in position and brought down the hammer.
16:30And it broke.
16:31Not the diamond, the blade.
16:33So, he got another blade and put that in position.
16:38Brought down the hammer.
16:40And as he struck it, Jacob Asher fainted.
16:44When he came round, the diamond had split perfectly in two.
16:49And from there, Jacob Asher went on to cut the diamond into 105 different brilliant cut diamonds.
16:56103 of those diamonds, Jacob Asher received for his fee.
17:02Over two-thirds of the original stone.
17:05And just two diamonds were returned to King Edward and were set in the crown jewels.
17:12These are replicas of the crown jewels.
17:27And here is the imperial state crown,
17:31which is worn by the Queen at special functions like the opening of Parliament.
17:36Set here at the front is a model of the second largest diamond in the world
17:41called the Lesser Star of Africa.
17:43It's 317 carats.
17:46But in the scepter that the Queen holds,
17:50it's the largest diamond in the world by far.
17:54From the Cullinan diamond, it's 530 carats.
17:58And it's nearly twice as big as any other diamond in the world.
18:02Now, apart from diamonds, there's a metal that's always had great value.
18:13And that metal is...
18:15Gold.
18:24Now, why is gold so valuable?
18:27Well, for several reasons.
18:28One, it's reasonably scarce.
18:30Two, it's easily recognisable.
18:33Three, it doesn't corrode and it's not affected by acids.
18:36And four, it's easily shaped.
18:39In fact, gold can be beaten into a sheet just two millionths of an inch thick.
18:45And I have here a sheet of glass which is coated with gold two millionths of an inch thick.
18:52And you may not be able to see it,
18:54but perhaps you can see the difference in colour of this white card.
18:59Now, why put gold on glass?
19:06Well, seven layers of gold are contained in the windscreen of Concord.
19:15So that when it flies at height, the gold filters out the harmful rays of the sun.
19:22Now, every year, about 50 million ounces of gold are dug out of the ground.
19:30And a great proportion of that is transported halfway across the world and buried again.
19:36Gold bullion.
19:37And gold bullion, like diamonds, has a particular shape.
19:41Shape of the gold bar.
19:44Now, if this gold bar were real, it would be very heavy.
19:48And I'd have to struggle to get it out of the cupboard and carry it.
19:51I'd have to do this.
19:52I'd have to go...
19:53And struggle across the studio with it.
20:01And probably have to get somebody to help me.
20:04Who'd like to help me?
20:05Would you?
20:06All right, take that.
20:10Is it heavy?
20:11Put it on your knees.
20:13It is heavy because it's absolutely real.
20:18This is a solid gold bar.
20:21It weighs 12 and a half kilos or 27 pounds.
20:27As you see, can you try and lift it?
20:31No, you can't lift it.
20:33Oh, that's amazing.
20:33It's not too heavy.
20:34Now, last time we checked, this gold was valued at £37,529 and 86p.
20:45Which would buy a lot of sweets, wouldn't it?
20:47But you couldn't take this to a sweet shop or even a bank.
20:51Because if we turn it over...
20:54Oh!
20:54I'm sure it's too heavy.
20:55And look on the back.
21:00You see, there are words.
21:02Rand Refinery Limited.
21:03That's where it was made.
21:05And some figures here showing the fineness or purity.
21:07It's 99.68% pure gold.
21:12And here, PQ879, is a registration number, just like the registration of a car.
21:20So that anyone in the gold business, anywhere in the world, would know immediately where this gold bar came from.
21:26The amazing thing is that if all the gold in the world were gathered together, it would all fit into a room 70 feet by 70 feet by 70 feet high.
21:44I think it's time for a puzzle.
21:52Who's going to help with the puzzle?
21:53You are.
21:53Lovely.
21:55Right.
21:55Can you do a ripple shuffle?
21:57Yeah.
21:57Lovely.
21:58Okay.
21:59Now, if you look at those cards, they're alternately red, black, red, black, red, black, all the way through.
22:05Okay.
22:06So I'd like you to do a ripple shuffle.
22:09Split them in half and shuffle them together.
22:14You missed.
22:15Try again.
22:17Can I make the corners overlap?
22:19Nearly.
22:20Have you done it?
22:21Yes.
22:21Put them together.
22:23Can I help?
22:23There you are.
22:25There you are.
22:25That's it.
22:26Square them up.
22:27Now, let's have a look inside.
22:29The pack.
22:30And we should see.
22:34Yes.
22:34See?
22:34Two red together, two black together.
22:36And so on.
22:37Okay.
22:37Now, if I gather them up, they're all mixed up, my fingers are educated and they'll tell when
22:43I'm touching a red and a black card.
22:45There's a pair now.
22:46Red and black.
22:47Red and black.
22:48Red and black.
22:49Red and black.
22:50Red and black.
22:50Red and black.
22:51Red and black.
22:52Red and black.
22:52Now, if I went all through the pack, they would all come out in pairs of red and black.
22:56Oh, isn't that amazing?
22:59Poison it.
23:05It's not amazing.
23:07It's not amazing.
23:07It's a trick that actually works itself.
23:10If you know how to do it, and if you'd like to know how to do it, drop us a line.
23:12Johnny Ball.
23:13Think of a number.
23:14BBC Television.
23:15London.
23:16W12.
23:168QT.
23:17But don't forget, stamped addressed envelope.
23:19Meanwhile, I better find me gold bar.
23:21Or else I'll have a terrible goat complex, because they might stop at adding me wages.
23:26And have me gold bar.
23:28They haven't got it?
23:30Who's got it?
23:31Oh, come on.
23:32Look on, he's got me gold bar.
23:35Oh, help.
23:36Look under your seats.
23:37Quick.
23:38Find it.
23:39Quick.
23:39Where is he?
23:40Oh.
23:42What?
23:46Goodbye.
23:47Until next week.
23:51I'll see you next week.
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