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Topic: Coin Toss (Read 1220 times) |
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flamingdragon
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You and your arch rival are competing for the same girl. After years of battling, you both decide to settle it by tossing a coin.
Your rival produces a coin, but you don't have one on you. You are certain that the coin your rival has produced is loaded, meaning it will come up with heads more than 50% of the time on average.
However, you arrange a fair contest, based purely on chance and not skill, by flipping the coin. How?
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"The fool doth think he is wise, yet the wise man knoweth himself to be a fool"
"He who commands the past, commands the future. He who commands the future, commands the past."
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towr
wu::riddles Moderator
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Re: Coin Toss
« Reply #1 on: Nov 29th, 2006, 1:06am » |
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In secret choose heads or tail, and lay down the coin showing your choice and cover it. Then your opponent chooses heads or tails. If he chooses the same as you he wins, otherwise he looses.
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Icarus
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Re: Coin Toss
« Reply #2 on: Nov 29th, 2006, 5:37am » |
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Flip the coin twice. If both flips are the same, discard them and flip two more times. Keep this up until the flips differ. If it comes up HT, then one wins. If it comes up TH, the other wins.
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"Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed? " - Anonymous
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flamingdragon
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Re: Coin Toss
« Reply #3 on: Nov 29th, 2006, 7:05am » |
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That second one was what I was looking for.
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"The fool doth think he is wise, yet the wise man knoweth himself to be a fool"
"He who commands the past, commands the future. He who commands the future, commands the past."
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Whiskey Tango Foxtrot
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Sorry Goose, it's time to buzz a tower.
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Re: Coin Toss
« Reply #4 on: Nov 29th, 2006, 7:06am » |
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That's the most common one. Towr's solution would work just as well were it not stipulated that the coin must be tossed.
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"I do not feel obliged to believe that the same God who has endowed us with sense, reason, and intellect has intended us to forgo their use." - Galileo Galilei
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Icarus
wu::riddles Moderator
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Re: Coin Toss
« Reply #5 on: Nov 29th, 2006, 7:16am » |
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(I moved this to Easy, because it really isn't a "what happened" type of puzzle.)
Next question: Would this approach work? Since the coin is biased towards heads, keep flipping the coin until it comes up tails. If it takes an even number of flips, one wins. If it takes an odd number of flips, the other wins.
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| « Last Edit: Nov 29th, 2006, 7:17am by Icarus » |
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"Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed? " - Anonymous
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Sjoerd Job Postmus
Full Member
Posts: 228
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Re: Coin Toss
« Reply #6 on: Nov 29th, 2006, 8:21am » |
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on Nov 29th, 2006, 7:16am, Icarus wrote:(I moved this to Easy, because it really isn't a "what happened" type of puzzle.)
Next question: Would this approach work? Since the coin is biased towards heads, keep flipping the coin until it comes up tails. If it takes an even number of flips, one wins. If it takes an odd number of flips, the other wins. |
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It's pretty much the same, except that player choosing tail would have more change.
First idea:
res = toss()
while ( res == "HH" || res == "TT" )
{
res = toss()
}
if ( res == "HT" )
{
Win = Archrival;
}
else // if ( res == "TH" )
{
Win = You;
}
Second idea:
res = toss()
while ( res == "HH" )
{
res = toss()
}
if ( res == "HT" )
{
Win = Archrival;
}
else // if ( res == "TH" || res == "TT" )
{
Win = You;
}
First: Toss two coins, until different. If different, the first toin cossed decides.
Second: Toss two coins, until not both head. If not both head, first toin decides.
I think it is clear that, in the first situation, we have a fair game, and in the second, you're chances are a bit higher than those of your nemesis.
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towr
wu::riddles Moderator
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Some people are average, some are just mean.
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Re: Coin Toss
« Reply #7 on: Nov 29th, 2006, 8:24am » |
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on Nov 29th, 2006, 7:16am, Icarus wrote:| Next question: Would this approach work? Since the coin is biased towards heads, keep flipping the coin until it comes up tails. If it takes an even number of flips, one wins. If it takes an odd number of flips, the other wins. |
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I think it'd only work for specific biases.
[e]nevermind, unless you count p(T)=0[/e]
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| « Last Edit: Nov 29th, 2006, 8:39am by towr » |
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flamingdragon
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Re: Coin Toss
« Reply #8 on: Nov 29th, 2006, 4:53pm » |
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on Nov 29th, 2006, 7:16am, Icarus wrote:| (I moved this to Easy, because it really isn't a "what happened" type of puzzle.) |
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I could make it into a what am I riddle as well. 
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"The fool doth think he is wise, yet the wise man knoweth himself to be a fool"
"He who commands the past, commands the future. He who commands the future, commands the past."
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