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Extra Credit Problem:
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Taedrin
Federal Navy Academy
Gallente Federation
#1 - 2011-10-21 02:20:18 UTC  |  Edited by: Taedrin
An intriguing challenge from a friend of a friend, which a group of us already solved.

A prince from Far, Far Away visits a castle with the intention of wooing the princess there. The castle has a (straight) corridor with 17 rooms lined side-by-side. Each of the rooms have two doors connecting each other (except for the rooms on the ends), and another door connected to the corridor. A guard stops the prince and tells him that the princess is one of these rooms. However, the prince is allowed to knock on only a single door from the corridor. If the princess is in the room, he will be able to woo her and live happily ever after. If the princess is not in the room, he must leave and come back tomorrow to try again. Every night, the princess moves to an adjacent room. She never spends more than a single night in a room at a time.

Unfortunately, the prince already has his plane ticket for his return flight in 30 days. Can the prince conquer the princess? Prove your answer to be correct.
Isometric Isotope
Republic Military School
Minmatar Republic
#2 - 2011-10-21 02:34:24 UTC
Taedrin wrote:
An intriguing challenge from a friend of a friend, which a group of us already solved.

A prince from Far, Far Away visits a castle with the intention of wooing the princess there. The castle has a (straight) corridor with 17 rooms lined side-by-side. Each of the rooms have two doors connecting each other (except for the rooms on the ends), and another door connected to the corridor. A guard stops the prince and tells him that the princess is one of these rooms. However, the prince is allowed to knock on only a single door from the corridor. If the princess is in the room, he will be able to woo her and live happily ever after. If the princess is not in the room, he must leave and come back tomorrow to try again. Every night, the princess moves to an adjacent room. She never spends more than a single night in a room at a time.

Unfortunately, the prince already has his plane ticket for his return flight in 30 days. Can the prince conquer the princess? Prove your answer to be correct.

this be the kinda riddles people make up when they are high on something
Kinda like the one about the lien guard and the truthful guard its a conundrum that has no real value other then making my head spin for your pleasure

Grazzles You have done this successfully

My cup Overfloweth with stale coffee!
Taedrin
Federal Navy Academy
Gallente Federation
#3 - 2011-10-21 02:36:24 UTC
Isometric Isotope wrote:

this be the kinda riddles people make up when they are high on something
Kinda like the one about the lien guard and the truthful guard its a conundrum that has no real value other then making my head spin for your pleasure

Grazzles You have done this successfully


I aim to please. I am merely reciprocating the pain and suffering that my Calc professor has inflicted upon me by tricking me into joining a mathematics competition on November 5th.
Surfin's PlunderBunny
Sebiestor Tribe
Minmatar Republic
#4 - 2011-10-21 03:20:57 UTC
The answer is you get Chuck Norris to kick in a door every night, eventually she'll run out of places to hide Pirate

"Little ginger moron" ~David Hasselhoff 

Want to see what Surf is training or how little isk Surf has?  http://eveboard.com/pilot/Surfin%27s_PlunderBunny
stoicfaux
#5 - 2011-10-21 03:23:05 UTC
Quote:
Can the prince conquer the princess? Prove your answer to be correct.


Yes, it is possible to conquer the princess. He just has to guess lucky within 30 tries. Or did you want to know if there was a 100% guaranteed method to find the princess?

Aside from bypassing the guard, asking the guard, etc., there is no 100% way to win because the prince and princess can always leapfrog each other: Prince checks room 1 while princess is in room 2. Next day prince checks room 2, but princess has moved to room 1.

Also, as you describe it:
* the end rooms (#1 and #17) have no doors to adjacent rooms,
* the rooms' two doors could open to the same room (room #4 has two doors to room #5, instead of one door to #3 and one door to #5


Pon Farr Memorial: once every 7 years, all the carebears in high-sec must PvP or they will be temp-banned.
Surfin's PlunderBunny
Sebiestor Tribe
Minmatar Republic
#6 - 2011-10-21 03:31:04 UTC
Actually screw the doors, just have Chuck Norris kick down the walls.

"Little ginger moron" ~David Hasselhoff 

Want to see what Surf is training or how little isk Surf has?  http://eveboard.com/pilot/Surfin%27s_PlunderBunny
Cherry Nobyl
Sebiestor Tribe
Minmatar Republic
#7 - 2011-10-21 03:45:47 UTC
Taedrin wrote:
An intriguing challenge from a friend of a friend, which a group of us already solved.

A prince from Far, Far Away visits a castle with the intention of wooing the princess there. The castle has a (straight) corridor with 17 rooms lined side-by-side. Each of the rooms have two doors connecting each other (except for the rooms on the ends), and another door connected to the corridor. A guard stops the prince and tells him that the princess is one of these rooms. However, the prince is allowed to knock on only a single door from the corridor. If the princess is in the room, he will be able to woo her and live happily ever after. If the princess is not in the room, he must leave and come back tomorrow to try again. Every night, the princess moves to an adjacent room. She never spends more than a single night in a room at a time.

Unfortunately, the prince already has his plane ticket for his return flight in 30 days. Can the prince conquer the princess? Prove your answer to be correct.


the smarmy answer is very similar to this

another smarmy answer is to observe from the hillside which window has the light in it and use that as a reference. a slight variation would be to rappel over the side of the castle through a window.

love knows no bounds, but it does flirt with the human equivalent of p/np.
Taedrin
Federal Navy Academy
Gallente Federation
#8 - 2011-10-21 03:47:15 UTC
stoicfaux wrote:
Quote:
Can the prince conquer the princess? Prove your answer to be correct.


Yes, it is possible to conquer the princess. He just has to guess lucky within 30 tries. Or did you want to know if there was a 100% guaranteed method to find the princess?

Aside from bypassing the guard, asking the guard, etc., there is no 100% way to win because the prince and princess can always leapfrog each other: Prince checks room 1 while princess is in room 2. Next day prince checks room 2, but princess has moved to room 1.

Also, as you describe it:
* the end rooms (#1 and #17) have no doors to adjacent rooms,
* the rooms' two doors could open to the same room (room #4 has two doors to room #5, instead of one door to #3 and one door to #5



You want to prove, or disprove the existence of a 100% guaranteed method to find the princess.

TO clarify - the end rooms have one door to their adjacent room. Each room has exactly one door to each adjacent room. There is nothing strange or special about the room's layout. the rooms are laid out as a straight line, and you can use the doors to travel through each room without needing to go into the corridor.

Your leapfrog argument is a nice, but does not constitute proof. I will even go so far as to say that it is flawed - what happens if the prince checks room #2 twice in a row?
Taedrin
Federal Navy Academy
Gallente Federation
#9 - 2011-10-21 03:52:17 UTC
Cherry Nobyl wrote:
Taedrin wrote:
An intriguing challenge from a friend of a friend, which a group of us already solved.

A prince from Far, Far Away visits a castle with the intention of wooing the princess there. The castle has a (straight) corridor with 17 rooms lined side-by-side. Each of the rooms have two doors connecting each other (except for the rooms on the ends), and another door connected to the corridor. A guard stops the prince and tells him that the princess is one of these rooms. However, the prince is allowed to knock on only a single door from the corridor. If the princess is in the room, he will be able to woo her and live happily ever after. If the princess is not in the room, he must leave and come back tomorrow to try again. Every night, the princess moves to an adjacent room. She never spends more than a single night in a room at a time.

Unfortunately, the prince already has his plane ticket for his return flight in 30 days. Can the prince conquer the princess? Prove your answer to be correct.


the smarmy answer is very similar to this

another smarmy answer is to observe from the hillside which window has the light in it and use that as a reference. a slight variation would be to rappel over the side of the castle through a window.

love knows no bounds, but it does flirt with the human equivalent of p/np.




I personally argued that the Prince should simply buy a gun and... negotiate... with the guard. But that was not deemed to be a correct answer for some reason Evil
stoicfaux
#10 - 2011-10-21 04:01:03 UTC
Taedrin wrote:
Your leapfrog argument is a nice, but does not constitute proof. I will even go so far as to say that it is flawed - what happens if the prince checks room #2 twice in a row?


The princess moves to room #4.

OTOH, there's an odd number of rooms, and the princess can be forced to be two rooms away, which means if you wait in room 1 for X time, you can... hrm... let me do some doodling.


Pon Farr Memorial: once every 7 years, all the carebears in high-sec must PvP or they will be temp-banned.
Alara IonStorm
#11 - 2011-10-21 05:05:31 UTC
Surfin's PlunderBunny wrote:
Actually screw the doors, just have Chuck Norris kick down the walls.

How does her having Sex with Chuck Norris help his case. He will never be able to satisfy her... ever after that.

The answer is obvious, man up and stab the guard in the face then knock on whatever door he damn well pleases.

Being bothered by the Help, he is a price for god sakes.
Isometric Isotope
Republic Military School
Minmatar Republic
#12 - 2011-10-21 05:42:28 UTC
obviously all he needs to do is create a stable worm hole generator and use that to go to her room Why knock when you can go where ever you darn well please lol

My cup Overfloweth with stale coffee!
Surfin's PlunderBunny
Sebiestor Tribe
Minmatar Republic
#13 - 2011-10-21 05:52:46 UTC
Can't we just dump the stuck up ***** and date some chick that doesn't sleep in a different room every night?

"Little ginger moron" ~David Hasselhoff 

Want to see what Surf is training or how little isk Surf has?  http://eveboard.com/pilot/Surfin%27s_PlunderBunny
Xercodo
Cruor Angelicus
#14 - 2011-10-21 06:04:14 UTC
This is as close as I can to coming up with a 100%...

The Guard said nothing about being able to use the doors within the rooms, only that he may use one from the corridor.

He tries the first door, if he is not lucky then he uses the doors from the other rooms to find the princess. But the guard's condition was that he can only woo her is he finds her via a corridor door. So he notes her current position and tries again the next day.

He waits until she is in an end rooms that her only possible direction to move is the one next to it and he can nab her there.

This solution has the flaw of the possibility of her never reaching an end room. Because of that possibility I claim that there is no 100% way to get to her because it is possible that even knowing her current position that he lucks out on the 50/50 chance every time.

The only way to guarantee success is to know she is on an end room.

The Drake is a Lie
Isometric Isotope
Republic Military School
Minmatar Republic
#15 - 2011-10-21 06:09:30 UTC
Xercodo wrote:
This is as close as I can to coming up with a 100%...

The Guard said nothing about being able to use the doors within the rooms, only that he may use one from the corridor.

He tries the first door, if he is not lucky then he uses the doors from the other rooms to find the princess. But the guard's condition was that he can only woo her is he finds her via a corridor door. So he notes her current position and tries again the next day.

He waits until she is in an end rooms that her only possible direction to move is the one next to it and he can nab her there.

This solution has the flaw of the possibility of her never reaching an end room. Because of that possibility I claim that there is no 100% way to get to her because it is possible that even knowing her current position that he lucks out on the 50/50 chance every time.

The only way to guarantee success is to know she is on an end room.

worm hole generator.... all he needs why bother even knocking or a cloning device clone him self a billion times and knock on every door that way :) but then he'd have to kill the clones and thats just messy business

My cup Overfloweth with stale coffee!
Taedrin
Federal Navy Academy
Gallente Federation
#16 - 2011-10-21 06:14:03 UTC  |  Edited by: Taedrin
Xercodo wrote:
This is as close as I can to coming up with a 100%...

The Guard said nothing about being able to use the doors within the rooms, only that he may use one from the corridor.

He tries the first door, if he is not lucky then he uses the doors from the other rooms to find the princess. But the guard's condition was that he can only woo her is he finds her via a corridor door. So he notes her current position and tries again the next day.

He waits until she is in an end rooms that her only possible direction to move is the one next to it and he can nab her there.

This solution has the flaw of the possibility of her never reaching an end room. Because of that possibility I claim that there is no 100% way to get to her because it is possible that even knowing her current position that he lucks out on the 50/50 chance every time.

The only way to guarantee success is to know she is on an end room.


Sadly, this is a loop hole due to the way I recounted the problem. I don't think the original wording allowed for this loop hole.

The "correct" answer takes advantage of no loop holes, or any non-linear thinking. It does not require any advanced or tricky mathematics. Once you see the proof, you will be surprised about how simple it is.

EDIT: Hint:

Is it possible for the prince to find the princess if there is only 1 room? How about 2 rooms? 3 rooms? 4 rooms?
stoicfaux
#17 - 2011-10-21 14:25:13 UTC
If the Prince selects room #2 twice in a row, then he is guaranteed that room #1 does not contain the Princess. I think the trick is going to requiring relying on the fact that the Princess must move every night.

For example:
If the prince (M for male) selects door 2 on day 1 (T for turn,) and the Princess (F for female) happens to be in room 1. On turn two, the Princess must move to room 2. By selecting room 2 two days in a row, the Prince either catches the Princes or can guarantee that the Princess is not in room 1.

If the prince (M for male) selects door 2 on day 1 (T for turn,) and the Princess (F for female) happens to be in room 3, then by selecting room 2 again, then the princess has to move to room 4 (or she moves to room 2 and is caught.)
T M F
1: 2 3
2: 2 4 (cannot move from room 3 to room 2, so must move to room 4)
3: 3 5 (cannot move from room 4 to room 3, so must move to room 5)
...
repeat until princess is cornered in room 17.

Once the princess is guaranteed to be two rooms away in a particular direction, then the Prince will find her assuming he has enough turns left.


However, you still have to worry about being leapfrogged, but you can compensate for that by jumping back two rooms:
T M F
1: 2 4
2: 2 3
3: 3 2 (Princess just leapfrogged the Prince)
4: 1 3 (Princess must move to room 4 next turn)
5: 2 4 (Princess is now two rooms away and will be caught)
6: 3 5
The Princess must move to room 3 on turn 4, which means she's two rooms away and will be caught.

I'm mostly sure that you can always catch the princess, but I still need to work out the pattern/formula for preventing leapfrogs for the proof.

Pon Farr Memorial: once every 7 years, all the carebears in high-sec must PvP or they will be temp-banned.
Myfanwy Heimdal
Heimdal Freight and Manufacture Inc
#18 - 2011-10-21 15:00:12 UTC
stoicfaux wrote:
If the Prince selects room #2 twice in a row, then he is guaranteed that room #1 does not contain the Princess. I think the trick is going to requiring relying on the fact that the Princess must move every night.

For example:
If the prince (M for male) selects door 2 on day 1 (T for turn,) and the Princess (F for female) happens to be in room 1. On turn two, the Princess must move to room 2. By selecting room 2 two days in a row, the Prince either catches the Princes or can guarantee that the Princess is not in room 1.

If the prince (M for male) selects door 2 on day 1 (T for turn,) and the Princess (F for female) happens to be in room 3, then by selecting room 2 again, then the princess has to move to room 4 (or she moves to room 2 and is caught.)
T M F
1: 2 3
2: 2 4 (cannot move from room 3 to room 2, so must move to room 4)
3: 3 5 (cannot move from room 4 to room 3, so must move to room 5)
...
repeat until princess is cornered in room 17.

Once the princess is guaranteed to be two rooms away in a particular direction, then the Prince will find her assuming he has enough turns left.


However, you still have to worry about being leapfrogged, but you can compensate for that by jumping back two rooms:
T M F
1: 2 4
2: 2 3
3: 3 2 (Princess just leapfrogged the Prince)
4: 1 3 (Princess must move to room 4 next turn)
5: 2 4 (Princess is now two rooms away and will be caught)
6: 3 5
The Princess must move to room 3 on turn 4, which means she's two rooms away and will be caught.

I'm mostly sure that you can always catch the princess, but I still need to work out the pattern/formula for preventing leapfrogs for the proof.



That''s excellent but the danger is that on the move before you go to Room 3 she moves to Room 4 from Room 5. Thus then next she she can either go back to Room 5 or leap frog you into Room 3 as you go to Room 4.

Pam:  I wonder what my name means in Welsh?Nessa: Why?
Zagam
Caldari Provisions
Caldari State
#19 - 2011-10-21 15:17:51 UTC
The riddle only says the prince can "knock" on one door.

Why not just open the freakin' door?
Myfanwy Heimdal
Heimdal Freight and Manufacture Inc
#20 - 2011-10-21 15:25:22 UTC
Zagam wrote:
The riddle only says the prince can "knock" on one door.

Why not just open the freakin' door?



"Who's that knocking on my door?
Who's that knocking on my door?,
cried the fair young maiden
"It's only me from across the sea,
Said Barnacle Bill the Sailor."



Best stop here before the forum's PhilopKDock cuss-o-filter kicks in.

Pam:  I wonder what my name means in Welsh?Nessa: Why?
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