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Maths problem: 2/9/2013 14:59:49

hedja
Level 58
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Does anyone know what the rule of this maths sequence is? If you think you do say what you think the next 1 will be :D

1
11
21
1211
111221
312211
13112221
1113213211

If you get it right, can you also prove why there will never be a number 4 in ANY sequence, no matter how many you do.
Maths problem: 2/9/2013 15:07:57

Level 59
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say what you see.

in the first row i see one number 1 so i say 11, then i see 2 number ones so i say 21 etc so the next is 31131211131211.

you want a proof? you sound like sze. I will give you some latex but i am too drunk to write you a proof. no 4s because you cant get 4 of anything in a row

duh.
Maths problem: 2/9/2013 15:33:13

Ravera
Level 44
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31131211131221

piggy/tigger had the second last number wrong :P
Maths problem: 2/9/2013 15:35:08

hedja
Level 58
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damn, you guys are too clever :P

If anyone else has maths problems (fun / interesting) then please post :)
Maths problem: 2/9/2013 15:56:15

Seahawks
Level 51
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what pattern can be notice in the sequence (dont just say how each line is made, but say what they all have in common)
1
11
121
1331
14641
1510105
also give the next number
Maths problem: 2/9/2013 15:56:46

Seahawks
Level 51
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last one has a 1 at end
Maths problem: 2/9/2013 16:09:19

Turing
Level 46
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It's pascal's triangle.
Maths problem: 2/9/2013 16:14:16

Level 59
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Try coming up with something original.
Maths problem: 2/9/2013 16:31:41

Seahawks
Level 51
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im asking for what all have in common, not what it is.
Maths problem: 2/9/2013 16:38:06

Level 59
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Maths problem: 2/9/2013 16:46:42

Seahawks
Level 51
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sighs, im asking for whats unusual about every number, not how to solve it or what it is called
Maths problem: 2/9/2013 16:55:27

Level 59
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Nothing is unusual about every number, do you mean something like, theyre all prime?
Maths problem: 2/9/2013 18:56:04

Z-Dog
Level 54
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Each row is a combination of nCr where n is the row number (starting at 0) and r is that number's position in the row (starting at 0).
Maths problem: 2/9/2013 19:59:43

Seahawks
Level 51
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sigh, they are all powers of 11
Maths problem: 2/10/2013 04:34:52

nich
Level 59
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Someone's bound to post this eventually so it might as well be me, I've altered some things to hopefully make it slightly less google-able.

Suppose you're on a cruise ship, and you're given the choice of three boxes: inside one box is a super-deluxe pogo stick; the others contain radishes. You choose a box, say No. 1, and the host, who knows what's inside the boxes, opens another box, say No. 3, which has a radish. He then says to you, "Do you want swap your box for box No. 2?" Is it to your advantage to switch your or keep your original box? Or is there no difference?

Also you definitely want the super-deluxe pogo stick instead of a radish.
Maths problem: 2/10/2013 04:40:02

Seahawks
Level 51
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you want to switch, this is the famous monty hall problem. Look up how to do it online but i will give you the basics. at the beginning they each have a 1/3 chance, and then the host shows you one that does not have it. Because he intentionally did this then there is still a 1/3 chance for the one you picked and a 2/3 chance for the one you did not pick
Maths problem: 2/10/2013 04:44:24

nich
Level 59
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Correct, I was hoping for someone who hadn't already heard of it though...
Maths problem: 2/10/2013 04:54:54

Seahawks
Level 51
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oh sorry :P
next problem: there are two envelopes and one has twice as much money in it than the other does you open one envelope and it has 50 dollars in it. do you want to keep the fifty dollars or take the amount of money that is in the second envelope and why?
Maths problem: 2/10/2013 07:04:35

Clifford The Big Red Dog
Level 37
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25x.5+100x.5= 62.5 open the second
Maths problem: 2/10/2013 09:09:18

his balls.
Level 60
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If you get to see the amount of money the point to this paradox is lost. You swap and see whether you were right to swap and the game stops there.

The classical problem is you get the envelope and then without seeing what's inside are asked whether you want to swap. Some say your expected return by swapping is greater then by sticking so you swap. You are then asked whether you want to swap again and the same logic apples so you swap. Basically you might conclude that it is beneficial to swap indefinitely. Clearly it is not so we have a paradox.

Maths is funny sometimes. It is 50 50. You shouldn't hurt your brain by overanalysing.
Maths problem: 2/10/2013 17:09:57

Z-Dog
Level 54
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That Monty Hall problem has always bothered me.
Maths problem: 2/10/2013 17:10:12

Seahawks
Level 51
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i thought it was clear if you swap then you keep the amount of money you swapped for and the point of having a set amount is that you always want to swap
Maths problem: 2/10/2013 17:20:19

x
Level 58
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This isn't the Monty Hall problem.

In the Monty Hall problem there are 3 doors. Two have no prizes, one has some valuable prize. You choose one, and the host removes an empty door from the two unchosen ones. You then have the option to swap, and you should always swap.

I understood it pretty quickly after reading about it and thinking it through, but apparently lots of people can't fathom it at all.

The one in this thread is simpler, because even though the chance of gaining or losing is 50-50, the potential loss is \$25 but the potential gain is \$50. It's more like a psychological test: if you can't get it, you just aren't much of a risk-taker.
Maths problem: 2/10/2013 17:26:03

Z-Dog
Level 54
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Even though it works out logically, the answer is so unintuitive.
Maths problem: 2/10/2013 17:27:52

Seahawks
Level 51
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nich's problem was the monty hall problem, not mine
Maths problem: 2/10/2013 18:26:07

x
Level 58
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:( herp
Maths problem: 2/10/2013 18:34:26

Najdorf
Level 46
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For the Robertson Hotel doesn’t merely have hundreds of rooms — it has an infinite number of them. Whenever a new guest arrives, the manager shifts the occupant of room 1 to room 2, room 2 to room 3, and so on. That frees up room 1 for the newcomer, and accommodates everyone else as well (though inconveniencing them by the move).

Now suppose infinitely many new guests arrive, sweaty and short-tempered. No problem.

How does he do it?

Later that night, an endless convoy of buses rumbles up to reception. There are infinitely many buses, and worse still, each one is loaded with an infinity of crabby people demanding that the hotel live up to its motto, “There’s always room at the Hilbert Hotel.”

The manager has faced this challenge before and takes it in stride.

First he does the doubling trick. That reassigns the current guests to the even-numbered rooms and clears out all the odd-numbered ones — a good start, because he now has an infinite number of rooms available.

But is that enough?

Note: learend this in a cantor lecture, you can look it up on google but don't ruin the fun
Maths problem: 2/10/2013 19:15:13

x
Level 58
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For the Robertson Hotel [...]

demanding that the hotel live up to its motto, “There’s always room at the Hilbert Hotel.”

Robertson should rethink their motto, it will drive away business.
Maths problem: 2/10/2013 22:27:31

his balls.
Level 60
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The Monty Hall Problem - you should swap, its intuitive and easy to prove.

I have no idea x how you can say that the two envelope problem is easier. Surely you are not suggesting that it is mathematically provable that you should swap. Swapping is just the same as picking the other one first a sticking. It is for sure of no benefit to swap, the difficulty is in proving it. Very tricky.
Maths problem: 2/10/2013 22:34:57

his balls.
Level 60
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