A town consists of only one street in the form of a circle. The town authorities give out four licenses for a particular kind of business. The inhabitants of the town live in equal density along the circle and will always go to the closest business for what they need. Business A gets to choose a location first, then business B, then C, and finally D. Each business desires to carve out as much business for themselves as possible but each knows the others all have the same motive. Assume that if a business is indifferent between locating in two different sections of the circle it will choose a section at random. Also assume that the business that goes last will choose a location in the middle of the largest (or one of the largest) sections. Where should business B choose relative to the location of A?
AND
you are a cook in a remote area with no clocks or other way of keeping time other than a 4 minute hourglass and a 7 minute hourglass. You do have a stove however with water in a pot already boiling. Somebody asks you for a 9 minute egg, and you know this person is a perfectionist and will be able to tell if you undercook or overcook the eggs by even a few seconds. What is the least amount of time it will take to prepare the egg?
I think it's like u put 7 min hourglas + 4 min hourglass and when the 4 min'er runs out u got 3 mins left on the 7 min'er. And there u cook the egg for 3min time. And then u repeat this 2 times more
i get it but its doesnt seem to have an answer. A chooses a random spot. Any spot that B would choose would split the profits fro mthe whole circle equaly but knowing that everybody wants the same it would choose 180 degrees away spot. Then C exacly between A and B. Doesnt matter which way and D 180 degrees from C. This way the profits are the same and the shops are 90 degrees away from each other clockwise starting from A it would be: A, C, B, D or A, D, B, C.
hmm, I get it how u think it, but still there's something strange about it. I mean, if each of them wants to have most customers, why would they setup equally if they are setting up in a certain order?
Shouldn't each of them try to be the closest place for as many ppl as possible. And B can't know which spots C and D will pick, so B should try to cover as much area as possible only when A is present ... But still your solution might be right...
maybe I understand it wrong but I got the idea like A wouldn't know that there will be anymore contenders, and B knows A but doesn't know there will be C and D. Consequently C knows of A and B but wouldn't know that there will be also D and D would know of them all.
And that's why I thought A can pick any place, because all the market will be for it only anyway. B will pick a spot where it could dominate A (actually the center point of the circle), and C will pick the next best spot where it will get most markets etc... but maybe I really understand it wrong... it's 6 am here already :p
1 - no idea, its 4.21 in the morning
2 - 21 minutes but not Spirea's way since you'd need to take it out for 4 minutes to reset the hourglasses. You do it this way. You set 4 min clock 3 times in a row and 7 min clock 2 times in a row. When 4 min clock time's off you have 2 minutes on 7 min clock. You start cooking the egg and with another 7 minutes counted you have it done. voila :p
the point is, u need to measure the exact time of 9 mins. So u need time to set up the system for that. Actually u need 12 more minutes before u can start cooking the eggs with this setup
2nd: 16 min.. It takes 7 minutes to make 4min hourglass to a 1min hourglass. After that use the 1min hourglass and then 4min hourglass twice. 7+1+4+4=16
A town consists of only one street in the form of a circle. The town authorities give out four licenses for a particular kind of business. The inhabitants of the town live in equal density along the circle and will always go to the closest business for what they need. Business A gets to choose a location first, then business B, then C, and finally D. Each business desires to carve out as much business for themselves as possible but each knows the others all have the same motive. Assume that if a business is indifferent between locating in two different sections of the circle it will choose a section at random. Also assume that the business that goes last will choose a location in the middle of the largest (or one of the largest) sections. Where should business B choose relative to the location of A?
AND
you are a cook in a remote area with no clocks or other way of keeping time other than a 4 minute hourglass and a 7 minute hourglass. You do have a stove however with water in a pot already boiling. Somebody asks you for a 9 minute egg, and you know this person is a perfectionist and will be able to tell if you undercook or overcook the eggs by even a few seconds. What is the least amount of time it will take to prepare the egg?
2nd - 9minutes
OVER 9000
2nd - not sure if I understood this correctly either but 21 mins
Edit: explanation below :p
ok I see the edit... basically the idea is the same anyway :)
but I wasn't lucky, just didn't apply it for practical use like u did :D
anyway, do u understand what the first question means even?
EDIT: how the fuck do you cook anyway? in parts? :D
Shouldn't each of them try to be the closest place for as many ppl as possible. And B can't know which spots C and D will pick, so B should try to cover as much area as possible only when A is present ... But still your solution might be right...
If B would choose location closer than 180 degrees away C and D would make B's profit the smallest or 2nd smallest. Cant be arsed to draw it tho xd
And that's why I thought A can pick any place, because all the market will be for it only anyway. B will pick a spot where it could dominate A (actually the center point of the circle), and C will pick the next best spot where it will get most markets etc... but maybe I really understand it wrong... it's 6 am here already :p
2 - 21 minutes but not Spirea's way since you'd need to take it out for 4 minutes to reset the hourglasses. You do it this way. You set 4 min clock 3 times in a row and 7 min clock 2 times in a row. When 4 min clock time's off you have 2 minutes on 7 min clock. You start cooking the egg and with another 7 minutes counted you have it done. voila :p
9 minutes.
HAHA DUMBASS
2nd: The answer is 9 minutes.
Well done
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