actually I am stuck on this Brain teaser. Any help is very much appreciated!
here it is: King Arthur, Merlin, Sir Lancelot, Sir Gawain, and Guinevere decide to go to their favorite restaurant to share some mead and grilled meats. They sit down at a round table for five, and as soon as they do, Lancelot notes, "We sat down around the table in age order! What are the odds of that?"
Merlin smiles broadly. "This is easily solved without any magic." He then shared the answer. What did he say the odds were?
Here is what I think: If you assume they all get seated at the same time then there would be 5!=120 possible seating option and sitting in age order is only one of them. But it didn't say in ascending or descending order, so there is 2. then 2 :(120-2) is 1: 59
However here is the answer: The odds are 11:1. (The probability is 1/12.)
Imagine they sat down in age order, with each person randomly picking a seat. The first person is guaranteed to pick a seat that "works". The second oldest can sit to his right or left, since these five can sit either clockwise or counterclockwise. The probability of picking a seat that works is thus 2/4, or 1/2. The third oldest now has three chairs to choose from, one of which continues the progression in the order determined by the second person, for a probability of 1/3. This leaves two seats for the fourth oldest, or a 1/2 chance. The youngest would thus be guaranteed to sit in the right seat, since there is only one seat left. This gives 1 * 1/2 * 1/3 * 1/2 * 1 = 1/12, or 11:1 odds against.
I agree with the answer but that only works if they are not seated at the same time, right?
what'd ya think?
It's a round table so if they are sitting oldest to youngest or youngest to oldest its the same thing. isn't it just 1(54321) * 5 because there are five ways of arranging that?
I think you are right! Thanks
There are 10 ways of seating them oldest to youngest (5 ways clockwise, 5 ways counterclockwise). There are 5! = 120 possible seating arrangements. Probability is 10/120, or 8.33%. I believe the OP was right.
isn't the total # of possibilities 4! ? permutations in a circle are " (n-1)! "
there are two ways of the correct arrangement (from right or from the left)
so 2/24 which equals 1/12 as the probability
At least that's the method of how I would have gotten it..
The answer is 2/4! or 1/12..since for a circle total number of permutations is (n-1)!. There are two ways ascending and descending, so 2/24 or 1/12
I was asked this in an SIG interview awhile back.
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