So we're going to talk about the origin, the mathematical origins of Tetris. The quite well-known computer game.
And
I
thought about this because recently I was on a holiday in Crete,
and I was walking down the side, with all these people selling, kind of, tourist rubbish.
But there was this guy who was selling these really interesting, like, math and logic puzzles - including this one here
which I bought. So this is a puzzle where it is full of these elements here,
which- these are not quite Tetris because Tetris is four squares, these have 5. So these are 5 squares.
So these are all the possible ways you can put 5 squares together, apart from this, and
rather brilliantly- so there are 12: 1, 2, 3, 4, 5, 6,
7, 8, 9, 10, 11, 12. There are 12 ways
you can put 5 squares together, and these are all the possible ones. And it turns out
that you can put them all together, and there's several ways to do it
but they're quite difficult to find, you can put them in at the square and all you need extra is the 4x4.
So this is the
the sort of the runt of the family.
Well, yeah, you can do it because you know that there are 12 and there are five of these, and so 5 times
12 is what?
(Brady: 60.) - Yes, 60 and 4 is 64, which is 8x8.
So obviously you know
the numbers are going to work, and it's just finding it and can it work?
And the reason why I wanted to buy this is because there is a person who is the first person to discover
that you can get all these things with 5 squares in, into a biggest 8x8 square: and his name was
Henry Dudeney, or Henry Ernest Dudeney,
known to his friends and friends as Ernest; who was Britain's greatest inventor of puzzles.
I would say the greatest inventor of mathematical puzzles the world has ever seen
because
the depth and the variety of the
mathematical puzzles that he did beats anyone else. And lots of Americans would say no it was Sam Loyd. Sam Loyd, they were contemporaries,
they actually hated each other. Well, they liked each other then they fell out so they hated each other.
Whereas Sam Loyd probably did more puzzles, was a bit more of
salesman, and he also did some amazing puzzles, but you don't find many mathematicians
studying Sam Loyd puzzles. But you find
still there are lots Dudeney puzzles that
people are interested in, including this one here. And this one first appeared in 1907 in a book called
The Canterbury puzzles, which all kind of had historical stories to them. And the story was, so William the Conqueror,
he's the person who came away from France and like invaded England, and then became King of England and he had two sons. And his sons
went to France and
stayed with the son of the French King at the time,
it's kind of just, sort of,
slightly apocryphal history. And apparently they got into a fight, and the fight was over a game of chess, because the British were beating the French.
Blows were
given. Basically they, yeah started fighting and
the chessboard was whacked over the head of someone and it
collapsed into thirteen different pieces. And the thirteen different pieces that are drawn in the 1907
Canterbury puzzles are exactly these pieces. And this is the first time in the mathematical literature that you have the selection of
all the possible
shapes that you can get when you put five, or in fact any number, of
squares
orthogonally next to each other. So I- they've got to be either sort of straight on, Dudeney
also did another puzzle ten years later
which was all about stamps and folding stamps. And there he said, what are all the different ways you can tear out four stamps together?
And that was the first time that there were ever the appearance of Tetris blocks. Because if you have four squares together,
that's what Tetris is. And so Dudeney, the first time ever
he did any type of block were the five ones in '07, and then in '17 there were the four ones. Now in the
1960s this American mathematician called Solomon Golomb
started looking at that, and started to classify them and do lots of maths on them. And he starts to call them
poly-ominoes. So the five one are
pentominoes, and this is the set of the fi- of 12 pentominoes.
There are tetrominoes, which are the ones with four. And there are the triominoes,
and then there's the Dominoes which are the one with the two. And it was because of
Solomon Golomb's work, in the 1980s a
Soviet
computer guy was reading Golomb's work - which, Golomb's work references Dudeney's work; and
basically invented Tetris, which is the tetrominoes
falling and you have to stack them. And, I dunno, this is basically - if it was called "Petris" this is basically what it would be like.
I got this because of the hor- the historical-ness of it, I thought isn't it interesting that this is the very puzzle that begat
Tetris. And Here I am, in Greece, and a guy's selling it. And so I bought it, and it is incredibly satisfying to do.
(Brady: Come on, let's see you do it.)
So, it would probably - takes me each time. 'Cause you always forget how you stack them.
And each time you do it, it probably takes me about 15-20 minutes? And you think until you've done it
there's no way I'm gonna be able to do it. And then when you get it, you just do get it.
And you sort of work out little techniques, you know,
these ones here like much more complicated so it's quite good to put that there.
And also there's another one, this one here gets in the way so I can often start with something like this.
Maybe let's put this in the corner.
It's so sort of tactile and it's lovely. And when you get it it's really, really, really satisfying.
We've made a second video about another famous Dudeney puzzle.
[Preview] What I want, I want you to get them there to
here in three moves.
Also
if you'd like to see more videos with Alex Bellos, or buy one if his excellent books about mathematics, including this one about puzzles,
there'll be a link down in the video description.
Thanks to everyone who supports Numberphile on Patreon like the people whose names you see on the screen.
If you'd like to join them, also there'll be links down in the description. Oh and here's the solution,
pretty easy, eh?