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the horse race one, if no one posted it yet:
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7 races
initial 5, where we eliminate the 2 slowes from each group. 15 horses remain.
then race all the winning horses.. winner is the fastest, the bottom two eliminated, and the 4 remaining horses that lost to the bottom 2 in the first race are eliminated. for the horse that came in 3rd the winners race, we can eliminate the horses that lost to him( 2 horses). we can also elimate the third place horse from the initial race of the horse who came in second in the winners race.. 2+4+2+1 = 9 horses eliminated.
6 horses remain, but the winner of the winners race does not have to race again. so 5 horses, one more race, top 2 are 2nd/third fastest.
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Sanya12364 Posts
On April 20 2012 15:06 Aelfric wrote:Wow you guys are fast, then lets try something harder: Show nested quote +You have 25 horses. When they race, each horse runs at a different, constant pace. A horse will always run at the same pace no matter how many times it races.
You want to figure out which are your 3 fastest horses. You are allowed to race at most 5 horses against each other at a time. You don't have a stopwatch so all you can learn from each race is which order the horses finish in.
What is the least number of races you can conduct to figure out which 3 horses are fastest?
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nice. This should be 7.
5 groups of 5 horses will race. (group race)
The winners of the 5 group races will race. (winner's race) (this will be the fastest horse)
In the final race (consolation race) race the 2nd, 3rd from the group of the fastest horse and the 2nd fastest horse from the group of 2nd fastest in the winners race, and the 2nd and 3rd fastest in winner's race. (1st and 2nd will be 2nd and 3rd respectively)
very elegant
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Sanya12364 Posts
A friend packed six ping pong balls for you, 3 orange, 3 white. He's placed them in three pockets of your sports bag. One pocket has two orange balls. One pocket has two white balls. One pocket has one white and one orange. You reach into one random pocket and pull out an orange ping pong ball. What's the probability of the other ball in the pocket being orange?
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The probability is 2/3.
Consider: You reach into one random pocket and pull out a ping pong ball. What is the probability that the other ball in the pocket is the same color?
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Does this really need a [SFW] tag? Imagine this situation:
A man is at work, browsing teamliquid.net. He sees the title "Riddles / Puzzles / Brain Teasers", but dares not click it for fear of the likelyhood of it containing content unsafe for work.
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On April 21 2012 03:07 TanGeng wrote:
A friend packed six ping pong balls for you, 3 orange, 3 white. He's placed them in three pockets of your sports bag. One pocket has two orange balls. One pocket has two white balls. One pocket has one white and one orange. You reach into one random pocket and pull out an orange ping pong ball. What's the probability of the other ball in the pocket being orange?
+ Show Spoiler +
Edit: I'm stupid.
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I would say 50 % for another orange ball.
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United States7483 Posts
If a chicken and a half can lay an egg and a half in a day and a half, how many eggs could six chickens lay in six days?
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On April 21 2012 03:07 TanGeng wrote:A friend packed six ping pong balls for you, 3 orange, 3 white. He's placed them in three pockets of your sports bag. One pocket has two orange balls. One pocket has two white balls. One pocket has one white and one orange. You reach into one random pocket and pull out an orange ping pong ball. What's the probability of the other ball in the pocket being orange? + Show Spoiler +
The probability is 2/3.
Consider: You reach into one random pocket and pull out a ping pong ball. What is the probability that the other ball in the pocket is the same color?
+ Show Spoiler +
Possibilities are:
Orange and Orange
Orange and White
White and White
If you pulls out a orange ball, there is only one scenario of the three where the second ball is also orange.
Therefore the odds of the second ball being orange is 33%.
Lol'd when I quoted you and found out you were wrong about your own answer.
Second part of your answer is the same, 33%.
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On April 21 2012 04:09 killa_robot wrote:Show nested quote +On April 21 2012 03:07 TanGeng wrote:A friend packed six ping pong balls for you, 3 orange, 3 white. He's placed them in three pockets of your sports bag. One pocket has two orange balls. One pocket has two white balls. One pocket has one white and one orange. You reach into one random pocket and pull out an orange ping pong ball. What's the probability of the other ball in the pocket being orange? + Show Spoiler +
The probability is 2/3.
Consider: You reach into one random pocket and pull out a ping pong ball. What is the probability that the other ball in the pocket is the same color?
+ Show Spoiler +
Possibilities are:
Orange and Orange
Orange and White
White and White
If you pulls out a orange ball, there is only one scenario of the three where the second ball is also orange.
Therefore the odds of the second ball being orange is 33%.
Lol'd when I quoted you and found out you were wrong about your own answer.
Second part of your answer is the same, 33%.
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I'm confused. You listed 3 scenarios. One out of the three scenarios has the second ball being orange. However, one of those scenarios has no orange ball in the first place. Therefore you need only consider Orange, Orange and Orange, White. Therefore you have 1 chance out of 2 choices, 50%.
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On April 21 2012 04:11 terr13 wrote:Show nested quote +On April 21 2012 04:09 killa_robot wrote:On April 21 2012 03:07 TanGeng wrote:A friend packed six ping pong balls for you, 3 orange, 3 white. He's placed them in three pockets of your sports bag. One pocket has two orange balls. One pocket has two white balls. One pocket has one white and one orange. You reach into one random pocket and pull out an orange ping pong ball. What's the probability of the other ball in the pocket being orange? + Show Spoiler +
The probability is 2/3.
Consider: You reach into one random pocket and pull out a ping pong ball. What is the probability that the other ball in the pocket is the same color?
+ Show Spoiler +
Possibilities are:
Orange and Orange
Orange and White
White and White
If you pulls out a orange ball, there is only one scenario of the three where the second ball is also orange.
Therefore the odds of the second ball being orange is 33%.
Lol'd when I quoted you and found out you were wrong about your own answer.
Second part of your answer is the same, 33%.
+ Show Spoiler +
I'm confused. You listed 3 scenarios. One out of the three scenarios has the second ball being orange. However, one of those scenarios has no orange ball in the first place. Therefore you need only consider Orange, Orange and Orange, White. Therefore you have 1 chance out of 2 choices, 50%.
+ Show Spoiler +This question is similar to the one I posted, and it really depends on how you interpret the question.
Interpretation 1: Say you reach into a random bag and pull out a random ball 30 times. 10 times you will pull an orange ball out of the OO bag, 5 times you will pull an orange ball out of the OW bag, 5 times you will pull a white ball out of the OW bag and 10 times you will pull a white ball out of the WW bag. You can see that in this case that out of the 15 times you pull an orange ball 10 times the other ball is also orange. Answer = 10/15 = 66%. You were more likely to reveal an orange ball form the OO bag than from the OW bag, so you are most likely reaching in the OO bag.
Interpretation 2: You always pull out an orange ball if possible because the question says you do. If you do this 30 times, 10 times you will pull an orange ball lout of the OO bag, 10 times you will pull an orange ball out of the OW bag and 10 times you will pull an White ball out of the WW bag. You will never pull a white ball out of the OW bag first in this interpretation of the question. You can see that out of the 20 times you pull an orange ball, 10 of those have another orange ball inside, so this gives an answer of 10/20 = 50%.
I wish there was an easier way of describing the randomness this type of question. For example, in Monty Hall style questions, it is always stated that the revealed choice is not random (interpretation 2).
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On April 21 2012 04:29 el_dawg wrote:Show nested quote +On April 21 2012 04:11 terr13 wrote:On April 21 2012 04:09 killa_robot wrote:On April 21 2012 03:07 TanGeng wrote:A friend packed six ping pong balls for you, 3 orange, 3 white. He's placed them in three pockets of your sports bag. One pocket has two orange balls. One pocket has two white balls. One pocket has one white and one orange. You reach into one random pocket and pull out an orange ping pong ball. What's the probability of the other ball in the pocket being orange? + Show Spoiler +
The probability is 2/3.
Consider: You reach into one random pocket and pull out a ping pong ball. What is the probability that the other ball in the pocket is the same color?
+ Show Spoiler +
Possibilities are:
Orange and Orange
Orange and White
White and White
If you pulls out a orange ball, there is only one scenario of the three where the second ball is also orange.
Therefore the odds of the second ball being orange is 33%.
Lol'd when I quoted you and found out you were wrong about your own answer.
Second part of your answer is the same, 33%.
+ Show Spoiler +
I'm confused. You listed 3 scenarios. One out of the three scenarios has the second ball being orange. However, one of those scenarios has no orange ball in the first place. Therefore you need only consider Orange, Orange and Orange, White. Therefore you have 1 chance out of 2 choices, 50%.
+ Show Spoiler +This question is similar to the one I posted, and it really depends on how you interpret the question.
Interpretation 1: Say you reach into a random bag and pull out a random ball 30 times. 10 times you will pull an orange ball out of the OO bag, 5 times you will pull an orange ball out of the OW bag, 5 times you will pull a white ball out of the OW bag and 10 times you will pull a white ball out of the WW bag. You can see that in this case that out of the 15 times you pull an orange ball the other ball is also orange. Answer = 66%. You were more likely to reveal an orange ball form the OO bag than from the OW bag, so you are most likely reaching in the OO bag.
Interpretation 2: You always pull out an orange ball if possible because the question says you do. If you do this 30 times, 10 times you will pull an orange ball lout of the OO bag, 10 times you will pull an orange ball out of the OW bag and 10 times you will pull an White ball out of the WW bag. You can see that out of the 20 times you pull an orange ball, 10 of those have another orange ball inside, so this gives an answer of 50%.
I wish there was an easier way of describing the randomness this type of question. For example, in Monty Hall style questions, it is always stated that the revealed choice is not random (interpretation 2).
+ Show Spoiler +I'm not entirely convinced of the solution, but I was just pointing out the flaw in his logic.
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Recently heard a neat twist on an old puzzle. The original puzzle:
Suppose you have 10 jars each with unlimited marbles. 9 of the jars contain marbles weighing 1 gram and one of the jars contains marbles weighing 1.1 grams. You have a digital scale that will tell you the exact weight of what you put on it. How can you tell which jar has the heavier marbles in 1 weighing?
The twist:
Now suppose that you don't know how many jars have marbles that weigh 1 gram and how many jars have marbles that weigh 1.1 grams (but you still have 10 really big (infinite) jars total). How can you tell which jars have heavier marbles in just 1 weighing?
EDIT: My mistake, the problem is more interesting if you assume you have fewer than 4000 marbles in each jar. The unlimited case is somewhat trivial.
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On April 21 2012 04:59 nq07 wrote:
Recently heard a neat twist on an old puzzle. The original puzzle:
Suppose you have 10 jars each with unlimited marbles. 9 of the jars contain marbles weighing 1 gram and one of the jars contains marbles weighing 1.1 grams. You have a digital scale that will tell you the exact weight of what you put on it. How can you tell which jar has the heavier marbles in 1 weighing?
The twist:
Now suppose that you don't know how many jars have marbles that weigh 1 gram and how many jars have marbles that weigh 1.1 grams (but you still have 10 really big (infinite) jars total). How can you tell which jars have heavier marbles in just 1 weighing?
+ Show Spoiler +
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On April 21 2012 03:07 TanGeng wrote:A friend packed six ping pong balls for you, 3 orange, 3 white. He's placed them in three pockets of your sports bag. One pocket has two orange balls. One pocket has two white balls. One pocket has one white and one orange. You reach into one random pocket and pull out an orange ping pong ball. What's the probability of the other ball in the pocket being orange? + Show Spoiler +
The probability is 2/3.
Consider: You reach into one random pocket and pull out a ping pong ball. What is the probability that the other ball in the pocket is the same color?
+ Show Spoiler +Since the wording of the problem says random pocket, the answer is 1/2. If it said random marble, the answer 2/3 would have been correct.
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On April 21 2012 05:04 LastPrime wrote:Show nested quote +On April 21 2012 04:59 nq07 wrote:
Recently heard a neat twist on an old puzzle. The original puzzle:
Suppose you have 10 jars each with unlimited marbles. 9 of the jars contain marbles weighing 1 gram and one of the jars contains marbles weighing 1.1 grams. You have a digital scale that will tell you the exact weight of what you put on it. How can you tell which jar has the heavier marbles in 1 weighing?
The twist:
Now suppose that you don't know how many jars have marbles that weigh 1 gram and how many jars have marbles that weigh 1.1 grams (but you still have 10 really big (infinite) jars total). How can you tell which jars have heavier marbles in just 1 weighing? + Show Spoiler +
So fast!
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On April 21 2012 03:25 BallerIndustries wrote:
Does this really need a [SFW] tag? Imagine this situation:
A man is at work, browsing teamliquid.net. He sees the title "Riddles / Puzzles / Brain Teasers", but dares not click it for fear of the likelyhood of it containing content unsafe for work.
The [SFW] tag means it's safe to view at work. If it were not, it would have the [NSFW] tag..
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On April 21 2012 05:07 LastPrime wrote:Show nested quote +On April 21 2012 03:07 TanGeng wrote:A friend packed six ping pong balls for you, 3 orange, 3 white. He's placed them in three pockets of your sports bag. One pocket has two orange balls. One pocket has two white balls. One pocket has one white and one orange. You reach into one random pocket and pull out an orange ping pong ball. What's the probability of the other ball in the pocket being orange? + Show Spoiler +
The probability is 2/3.
Consider: You reach into one random pocket and pull out a ping pong ball. What is the probability that the other ball in the pocket is the same color?
+ Show Spoiler +Since the wording of the problem says random pocket, the answer is 1/2. If it said random marble, the answer 2/3 would have been correct.
+ Show Spoiler +But the problem implies that after reaching into a random pocket, you also randomly select one of the two balls in that pocket (otherwise, how would you end up with a ball)? So in fact the problem is implying random ball, in which case the 2/3 interpretation would seem to be correct?
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On April 21 2012 03:52 Whitewing wrote:
If a chicken and a half can lay an egg and a half in a day and a half, how many eggs could six chickens lay in six days?
Here's what I got:
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6 days is 1.5*4. So 1.5 chickens will lay 1.5*4 eggs in 1.5*4 days.
Now 1.5*4 = 6 eggs
But there are 6 chickens, which is equivalent to 1.5*4. So multiplying 4 "groups" of 1.5 chickens by the output of each chicken group for 6 days, we get:
4*6 = 24 eggs! Cool puzzle, I hope that worked
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Sanya12364 Posts
On April 21 2012 05:07 LastPrime wrote:Show nested quote +On April 21 2012 03:07 TanGeng wrote:A friend packed six ping pong balls for you, 3 orange, 3 white. He's placed them in three pockets of your sports bag. One pocket has two orange balls. One pocket has two white balls. One pocket has one white and one orange. You reach into one random pocket and pull out an orange ping pong ball. What's the probability of the other ball in the pocket being orange? + Show Spoiler +
The probability is 2/3.
Consider: You reach into one random pocket and pull out a ping pong ball. What is the probability that the other ball in the pocket is the same color?
+ Show Spoiler +Since the wording of the problem says random pocket, the answer is 1/2. If it said random marble, the answer 2/3 would have been correct.
The semantics doesn't work your way. BTW, who's pulling out random marbles?
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On April 21 2012 03:52 Whitewing wrote:
If a chicken and a half can lay an egg and a half in a day and a half, how many eggs could six chickens lay in six days?
+ Show Spoiler +I don't think half a chicken is able to lay eggs. So it's just 1 chicken that lays 1.5 eggs in 1.5 days. Which basically means 1 chicken lays 1 egg per day.
Based on this 6 chicken would lay 6 eggs in a day and in six days that would be 36 eggs.
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EPT
