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I don't like this game.

Profesor Zvezdelina is so cute

"The first number is a". and I have a favourite colour of the alphabet.

also, the maximum of possible clones in the bottom row and leftmost colum is two, so plenty of greenland unfilled

7:30

Isn't that Zeno's Paradox?

I'm in middle school and I would have said the sum of the first row is two

vsause did a video on supertasks which relates to this

Don't free the clowns!!

Why did we asume the original mass is 2? (its like starting with 1 pebble and associating it with the mass number 2, even though we started with 3 pebbles) If there were 3 clones originally, may i start the mass at 3? Or maybe even 6?

It can't be done, even in an infinite # of moves, because the board still has a corner, and you can't put a clone in the corner.

Is it possible to free the clones in INFINITELY many moves?

Free the Clowns"Let's use the very first number you learned in school"

Seven!

"One"

Darn it!

Oh, those poor clown clones…

1:17 the right what?? bart fans?

Chezzboard

I tried to do this using a spreadsheet. You think it's simple enough, you get the first two out pretty easily, but the last one is desceptively tricky. You see that in order to get space for the clone, you need to duplicate this clone, but that is blocked by a third clone. Okay, so you duplicate the third one, then the second one, but then you realize that now the top part is blocked and you need to move that, so you go down the line, clone those, and you getmore and more blockages.

the clowns are disappearing again!

Freeing the clowns!

How many moves do you need to free two of the three prison cells?

The question was how to free the three prisoners from the prison.

The answer was fill all the space outside the prison with prisoners.

Now the prison is empty.

Greenland used to be a nice country until the infinite clowns came and used up all their two gasolines.

I love this explanation! So very clever!

And even if you had infinite turns, you'd still have to free the last clone… but there's no space… so you'd have to free up the area around it, which is just like freeing the original prison. So you'd have to free an infinite number of prisons, from the first to the infinitieth, in reverse order.

And by that point, I suppose the entire board would be empty except for the one in the corner, since all the clones outside the prison would have to be in some "infinite" zone outside of the problem.

Isn't it impossible to fill in the top right square of the infinite grid?

#ClownsLifeMatters

This explanation is well done, but for those who are unsatisfied with some of the mysterious hand-waving and infinity arguments, don't worry. Using a similar idea, the proof can still be done by arguing for an upper bound of an n-by-n sized chessboard, and showing that for all n, the total area enclosed in the n-by-n chessboard is always less than 4.

I don't like clowns. Specially if the they are clones. Damn cloned clowns!

This is like the chain-reaction game

So, damn, amazing! I hate most of maths but when it's explained like this I'd love to know more. Extremely helpful.

It feels like the proof mentioned in the video does not respect original rules of the game. The initial prison has 1,1/2 and 1/2. Now, one of the 1/2's splits into 2 quarters. But that disallows further splitting of the other 1/2, since for it to split, both its upper and right cells must be free! Hence, the 3rd row sum in the video cannot start with 1/4 :/

I don't get the series thing. You're adding a positive value to a total an infinite number of times. So shouldn't you end up with infinity?

Euclid would be proud of this proof! Pure, finite logic!

♥ I am positively in love

Why do the "weights" of the clones have to reduce by half when cloned? That's critical to the proof but seems like an arbitrary assumption.

what is with saying "clowns" again and again. STOP clowning around.

I saw this question first time in Arthur Engel's Problem Solving Strategies (Chapter 1), the Q was slightly different though, very slight.

Well done on question 6! Very impressive

make 1 move,wait a minute,make another move,wait half a minute and so on

game finished in 2 minutes

The answer is no, the Danish tried to populate Greenland and it didn't work at all.

Not too sure ?

If the rules say that no cloning allowed if the cell above or/and the cell to the right, then how is this [ 4:45 ] allowed?

Numberphile, after seeing your, well, 2nd video I think, doesn't that prove that the original problem is unsolvable? There are only 2 clones on the first row or column after all, so the greenland is less than that of the prison! Are there any explanations to this?

Brilliant solution, explained brilliantly.

i constructed a scenario where just the two clones trying to make room for the one clone will fill an indefinitely large square leaving only their original spots and an indefinitely long strip are clear, so this should definitely be impossible

if you can prove that (proving something impossible) is impossible, then that is a contradiction since you just proved something impossible

евала звезда

I'm a PC, I don't like infinity in mathematics (@,@")

Conway checkers is taking me on quite a journey

Should be called Freeing the CLOWNS. Much more fun.

I hav problems with the weighing methog. I would expect the square (1;1) to have the weight 1/2 since it gets weight 1/4 from two different squares. This would allow a much higher weight outside the prison than inside.

If moving each clone takes a seconds (where a=the number assigned to the square the clone is on) won't the game finish in 4 seconds?

Perhaps a simpler proof that you can't win would be this: the last move supposedly fills two holes but leaves one behind, but you can't fill that hole because you need two to make a move possible.

What a ridicules proof, i bet the original proof was difrent than just saying you cant doan infinat amout of moves.

Very elegant. Thank you very much. But now the new question: Can you free the clones in infinitely many moves? (With a one last move may be!) No! Because on the first row and the first column you can have at most two clones!

A deity can solve the game. You just need sufficient 'power' over reality to do so. The game can be solved when time changes into eternity. The reality of eternity will instantaneously free the clones then and forevermore.

That's not a pebble

Just wondering, but… is it possible to make it so that only one chip is left on the prison and that chip is on one of the "1/2" circle? Can't seem to do it :/

Not to be rude or anything but I think I figured out that it is possible it would just take a really long time to do

In reality, the sum does wind up equaling 2. The sum should equal 1.99999 repeating, which actually equals 2. So this problem should be solvable.

2S = S + 2

2S – S = 2

S – (S/2) = 1

Slap that bad boy in the old ti89 and save yourself the watch

I don't get it… I tried it and won… So how did I do the impossible?

Greenland is part of Denmark

Star Wars: the clown wars

A inverse geometric sequence is always convergent . The limiting function is always less than the whole. So they are not greater or equal to escape.

How about not cloning clowns in the first place?

I think this this is officially the most horrendus accent in the world.

If you had the ability to play it for an infinitely long period of time could you then solve it?

I don't understand why these clowns are in prison. What country is this?

It is also impossible to make sure that only one clone that is NOT the one at the bottom left remains in the prison. If you're truly interested in the proof, answer this comment

7:07 I

FINALLYUNDERSTOOD WHY 1+1/2+1/4+1/8+… IS 2! THANK YOU!9:27 not sure that bit of maths/algebra is right

Enough clowning around.

Very elegant solution.

im here mostly for clown comments

It would still not be possible to get all the clones out, even with infinite moves.

This is because when you make a move you cannot change the number of clones on the lowest row, or the leftmost column. So a maximum of two squares each on the lowest row and the left most column are occupied, with the others being empty.

Therefore you have to leave a non-zero amount of space in greenland empty, so the space the clones can occupy in greenland is less than 2.

I loved it

poor greenland…

"lets assign these squares numbers, and our numbers for the boxes are going to be 'a' and 'b'."

Wouldn't you do 1/3 before you do 1/4? Where does the forth piece go?

It's also worth mentioning that the first column and row can never be completely filled, in fact they'll be empty except for one stuck in the second row on the first column and one in the second column on the first row (or just one clone in it's original position in the bottom left corner) and one clone at the farthest end you've reached in both the first column and row. You don't really need to go any further because as stated in the video as soon as one square remains empty you know the sum cannot add up to a whole number. A fraction will always be left behind in the prison no matter how many moves you make.

If this still isn't clear: When starting you have three pieces all three HAVE to make a clone diagonally but only 2 can move vertically and 2 horizontally. Since none of the clones can jump down or to the right you cannot have more than 2 clones on the first row and column.

Just wanted to highlight this since in the video it doesn't demonstrate this and leads you to believe that all squares could be filled in an infinite game which simply isn't possible.

They are actually called "echoes" in the new Smash Bros.

So basically the only way to free the clow… sorry clones is to do it as a super task.

Moral of the story: Don't play games with mathematicians!

The first number I learned… oh that one is too long to even fit in a comment section or a video

Explanation: we want to prove the game is impossible.

Step 1) conspiracy theories on the total sum of the square

Step 2) discovering the deep algorithm inside the game

Step 3) say "the game is infinite, so it must be impossible"

What a beautiful solution. Bravo!

Rosanna Rosannadanna

How are you going to put a clone in the top right corner?

That's trippy

Stop clowning around

Я вообще нихуя блять не понял

You make me proud to be a bulgarian.

Jester from Critical Role?! 🤗

Insane Clone Posse!

This channel is Vsauce, but with maths, which makes me happy beyond reason

Heh, "pebbles". After "stones" from backgammon?

Or, you could just call them "checkers", as we do in my country. 🙂

The very first and crucial assumption a=2b seems completely arbitrary to me and a bit of a stretch. Surely this has been rigorously proven somewhere but that step did not make much sense to me, given how many different ways there are to fill up your board in practice.

Why does the clone of 1 is 1/2? Shouldnt it be 1?

FREE THE CLOWNS