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Riddle Answering; Someone asks a riddle, the one who answeres correctly has to ask the next.
Topic Started: Aug 20 2010, 11:31 AM (12,845 Views)
V
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Vivaciously Vexacious Vivification
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I sort of was expecting someone else to have done so, but I'll edit in a riddle in a moment.

Man I like solving riddles much more than coming up with them:

Four members of a band are walking to a night concert. They decide to take a shortcut, but must cross a bridge. Luckily they have one flashlight. Because of the varying size of their instruments, it takes each member a different amount of time to cross the bridge - it takes the first person one minute, the second person two minutes, the third person five minutes and the fourth person ten minutes. They must cross the bridge in pairs, traveling at the slower speed so if the one minute person went with the ten minute person, it would take a total of ten minutes. Since there is only one flashlight, one person must come back across the bridge, then another pair can cross. They only have 17 minutes to cross the bridge and still get to the concert on time. What order should they cross to get everyone across and get to the concert?
Edited by V, May 6 2011, 08:25 PM.
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amginE
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1 & 2 go
1 comes back
10 & 5 go
2 comes back
1 & 2 go

total time = 2 + 1 + 10 + 2 + 2 = 17
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V
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Vivaciously Vexacious Vivification
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Yep
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amginE
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You are at the Second Life Adventurer's tournament and they're having a special competition event between top ranked players.
Currently, you're watching the battle between rank 4 "Quicksilver" and rank 6 "Lionheart". They're going for a best of 7 series duel.
You want to make a 2000 gold bet that Lionheart is going to win (you watched him before and you think his skills more than make up for the difference in rank).
Unfortunately, the betting ring only accepts bets for each individual round in the best of 7.

Can you split your 2000 gold into individual bets for each round and still end up with 0 g if Lionheart loses and 4000 g if Lionheart wins?
Remember, in a best of 7, whoever first gets 4 wins is the overall winner, regardless if it's 4-0 or 4-3.

P.S. Names are completely made up.

P.P.S. Bets are unweighted and are all of the double-or-nothing variety.

Difficulty rating: 7/10 ?
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daystar
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devin, evil overlord.
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...it seems hard and it's late. if i do it it'll be tomorrow
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V
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Vivaciously Vexacious Vivification
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Do you make the bets for all the rounds at the start, or as each round goes?

And is it a sure-fire answer, or a best probability answer?
Edited by V, May 6 2011, 10:14 PM.
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daystar
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devin, evil overlord.
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you'll so get it before i do
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amginE
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one as each round goes, sure fire
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daystar
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devin, evil overlord.
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...i hate finding sure fire answers T.T
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V
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Vivaciously Vexacious Vivification
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Well I get a couple things;

I thought it was impossible until I realized that you probably get the bet payout immediately after the round, to use on subsequent rounds?
Even then, to satisfy the 4000 if win, 0 if lose requirement, you would have to bet 2000 on the last round of them going 3-3, such that 2000 is all you have to bet. But you can't assume they would go 3-3 so I don't get what the answer could be. If you bet any less than your full amount and Lion loses you wouldn't have 0 left over.

If you bet any amount prior to 3-3 you have the chance to lose in which case you would need to make up the money in order to make a bet that would get you 4k.
I just don't see how there is a sure-fire way to go about it, unless you like cover every round outcome possibility.
Edited by V, May 8 2011, 02:26 PM.
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amginE
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yes you get the payout immediately and you can use it on the next round.
yes, you need to cover every possibility. there's not as many as you might think though.
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daystar
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devin, evil overlord.
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wish i was the person getting the money...
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V
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Vivaciously Vexacious Vivification
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Idk I still don't see how it is possible. Specifically, if Lion wins the first three, it isn't possible to sure fire win 4000/lose 0. You have to bet 2k on round 4, but if he loses that one he can still win a later round. In fact off hand the only way to sure-fire win 4000 or lose 0 is if they go to a 3-3 tie. None of the other combinations can guarantee you to 4000 if he wins AND 0 if he loses. Or I'm just wrong.

Wait, unless by 0 do you mean you end with 2000? Because it should be possible to make it so if he wins you end with 4k and if he loses you end with 2k.
Edited by V, May 8 2011, 04:48 PM.
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Tetsuki
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hm.

1. 500 first round.
win: 2500 loss: 1500
2. 500 second round.
win/win: 3000 win/loss: 2000 loss/loss: 1000
3. 500
win/win/win: 3500 win/win/loss: 2500 loss/loss/win: 1500 loss/loss/loss: 500
4. 500
win/win/win/win: 4000 win/win/win/loss: 3000 win/win/loss/loss: 2000 win/loss/loss/loss:1000 loss/loss/loss/loss: 0
5. 1000
win/win/win/loss/win: 4000 win/win/loss/loss/win: 3000 win/win/loss/loss/loss: 1000 win/loss/loss/loss/win(win/win/win/loss/loss): 2000 loss/loss/loss/win/loss: 0
6. 1000
win/win/loss/loss/win/win: 4000 win/win/loss/loss/win/loss: 2000 win/win/loss/loss/loss/loss: 0
7.2000
win/win/loss/loss/win/loss/win: 4000 win/win/loss/loss/win/loss/loss: 0


The red bit doesn't fit in...
Edited by Tetsuki, May 8 2011, 05:52 PM.
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daystar
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devin, evil overlord.
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...you got it!?
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Tetsuki
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no it isn't flawless. The red bit doesn't fit.
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V
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Vivaciously Vexacious Vivification
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I don't think those are all the combinations. For example win/win/win/loss/loss/loss/win doesn't work under those conditions. There are a few others too. But that's not bad for a start.

EDIT Just realized that is the red one. But loss/loss/loss/win/win/win/loss doesn't work either.

Also win/win/win/loss/loss/win
and loss/loss/loss/win/win/loss
Edited by V, May 8 2011, 06:46 PM.
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amginE
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interesting ideas everyone, but you guys aren't approaching the problem correctly.

don't think about all the different win/loss combinations. there's too many of them.
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daystar
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devin, evil overlord.
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...then should we think of the numbers 4000 and 0?
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amginE
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4000 and 0 are definitely important, but not quite what i meant.
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daystar
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devin, evil overlord.
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How about the number of wins and losses?
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Tetsuki
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@V: all of your examples are baesd on the red one. Like I said the red doesn't fir in. btw. doesn't come to the correct answer. All possiblitys should be in because you can change the first 4 like you want and based on the red one all resulting out of that one wouldn't come to the correct answer.
Edited by Tetsuki, May 9 2011, 01:19 AM.
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Tetsuki
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you can't know if and when she will loss/win. So how should the number be of any importance...
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V
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Vivaciously Vexacious Vivification
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V
May 8 2011, 04:46 PM
Idk I still don't see how it is possible. Specifically, if Lion wins the first three, it isn't possible to sure fire win 4000/lose 0. You have to bet 2k on round 4, but if he loses that one he can still win a later round. In fact off hand the only way to sure-fire win 4000 or lose 0 is if they go to a 3-3 tie. None of the other combinations can guarantee you to 4000 if he wins AND 0 if he loses. Or I'm just wrong.

Wait, unless by 0 do you mean you end with 2000? Because it should be possible to make it so if he wins you end with 4k and if he loses you end with 2k.
What about my last line there. Is that what you meant?
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daystar
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devin, evil overlord.
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i bet not, it wouldn't be ranked 7/10 if that was the case; amginE's rankings are no joke.
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Tetsuki
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hm,

still have no Idea how it could be.

Can I only bet on the lion or on the other one too?
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daystar
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devin, evil overlord.
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since you expect the lion to win you wouldn't bet on the other
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amginE
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It is impossible to come up with a strategy that would always end up with 2000 if you lose and 4000 if you win, unless you are somehow psychic.
It's a zero sum game.

And it doesn't really matter who you bet on. You can bet on the lion if you want but it doesn't change anything.
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daystar
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devin, evil overlord.
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...it's the numbers that count. not you betting or anything.
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daystar
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devin, evil overlord.
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If he doesn't win for some battles, he will lose. How many?
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Yuki
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zzz........my brain's overfried just from looking at Tetsuki's possible answers.....@@
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daystar
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devin, evil overlord.
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You should try and tacle a charting problem this could involve
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Yuki
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even if i do make a chart, I still won't get it cos I suck at maths.......-_-"
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daystar
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devin, evil overlord.
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i would chart it but my branches keep running into each other TT
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Yuki
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LOL that means your horrible at making charts!?
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apoptoxin4869
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OH GOD BRAIN RAPE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! WHY CAN'T THESE BE AS EASY AS THE BEGINNING???????????????? im stupid D: sad fais
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daystar
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devin, evil overlord.
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^agreed

@yuki: yeah, this is my first chart
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Yuki
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daystar, you never use charts in microsoft word before?
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apoptoxin4869
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excel is bettarrrrrrrrrrrrrrrrrrrrrrr but it gets confuzzling sometimes
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daystar
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devin, evil overlord.
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nope, never
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Yuki
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.......seriously?? You've never tried it before?
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daystar
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devin, evil overlord.
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i only knew about it recently
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Yuki
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.....I guess that's one of the disadvantages of being home-schooled.....
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Tetsuki
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We should get back to the topic...

@amginE: Could you give us some kind of clue?
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Yuki
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true.....we're stuck here....-_-"
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kycse
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Okay first here's a visualization of Testukis' Graph. The left path meaning win, the right path meaning lost. (And I know my handwriting is bad... And I really wish I had a whiteboard, I love writing on them, pacing around thinking and watching at my scribbles every now and then. )

Posted Image
Original Size

There's one thing I noticed. Did amgine ever said that you have to bet always the same, regardless in what kind of case you are? For example you could use tetsukis' earlier approach and just tweak it with "if we are in the win/win/loss case place a bet of x" instead of betting always a fixed amount each round. However I can't think of a tweak like that at that point, so there have to happen some at least a bit earlier.

But amgine said that we approach this kinda wrong. However I think a bottom up approach won't work here as well. And while trying every possible combination and bruteforcing it should be possible, I advise against it. It's no fun if you do that. And as amgine said, a lot of them actually end up in the same state.

But amgine, thanks you just saved my sunday. At least I have something to think about now. <3

Edited by kycse, May 28 2011, 05:19 PM.
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Tetsuki
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kycse
May 28 2011, 05:18 PM
There's one thing I noticed. Did amgine ever said that you have to bet always the same, regardless in what kind of case you are? For example you could use tetsukis' earlier approach and just tweak it with "if we are in the win/win/loss case place a bet of x" instead of betting always a fixed amount each round. However I can't think of a tweak like that at that point, so there have to happen some at least a bit earlier.
That would take a hell lot of time...

But I just don't get another idea.
Edited by Tetsuki, May 28 2011, 05:57 PM.
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amginE
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kycse is getting closer, the diagram should be helpful. and no, you can bet however you like.
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kycse
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I just got it, amgine you are great! Equivalence classes all the way do the trick! I'll write another diagram, cause visualization works really well with this :D

Okay, let's do this:

First our approach with win or loss was more or less totally wrong (well, at least in my approach it was.) We need to think in # of wins and # of losses. Therefore 0/0 will mean, 0 wins and 0 losses.
Okay, let us visualize what we know then:

Posted Image
Original Size

Okay. This is the Graph, left means win, right means loss. The circled states are our final states, when we get there we've either won or lost, and therefore we know how much gold we have at those states. for 4/X states that's 4000 and for X/4 states that's 0. And we know that we have 2000 at the beginning of this, the 0/0 state. Now we can calculate all the other states by adding the values of their two childs and divide them by two.
Example:
3/3's childs are 4/3 and 3/4 -> 4000 + 0 / 2 = 2000.

Posted Image
Original Size
edit: Just noticed that 0/1 is 1375 and not 1325...

This is what the graph looks like when we write the "current amount of money" under the respective state. To calculate the bet per round you have to subtract from the value of the current state the value of it's right child:
0/0 - 0/1 = 2000 - 1375 = 675, so 675 gold is the bet in the first round. For all states that makes:

250: 3/0, 0/3
500: 2/0, 0/2, 3/1, 1/3
625: 0/0, 1/0, 0/1
750: 1/1, 2/1, 1/2
1000: 2/2, 3/2, 2/3
2000: 3/3

And then we will end up at either 0 or 4000.
Edited by kycse, May 29 2011, 10:04 AM.
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Tetsuki
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didn't think of that.
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