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

Can the prince conquer the princess? Prove your answer to be correct.

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.

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

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.

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?

Actually screw the doors, just have Chuck Norris kick down the walls.

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.

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.

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.

The riddle only says the prince can "knock" on one door.

Why not just open the freakin' door?

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.

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 won't actually work. Nothing says the princess has to only move in one direction. She could quite easily just flip-flop between rooms 16 and 17, always moving back to the other, while you keep knocking on room 1.

My first through would be to walk up and down the corridor calling for her, then only knock on the door where she answers, but I suspect that's not allowed.

So, question 1: can you look through the keyholes?

Question 2: can you hear, once inside a room, if an adjacent room is occupied? If yes, then it's easy. Start at room 2, and see if either rooms 1 or 3 is occupied by the princess. If yes, knock on 2 again the following night. If she was in 1, you've caught her. If she ways in 3, there's a 50% chance you caught her and a 50% chance she's now in 4. If neither 1 nor 3 was occupied the first day, move to 3 the following day, and proceed down the corridor on successive days until the adjacent room has an occupant. Any time you do, knock on the same door the following day. Eventually she'll either move into the room you've chosen that day and you win, or you'll trap her at the far end and force her to choose your room. Either way you finish before the 30 days expires.

You are exactly half way there. However, you have taken a wrong turn with trying to prevent the princess from leapfrogging you.

Here's another hint: if the princess is able to leapfrog you, her location has a certain property depending upon the "turn" it is. Think evens and odds.

That won't actually work. Nothing says the princess has to only move in one direction. She could quite easily just flip-flop between rooms 16 and 17, always moving back to the other, while you keep knocking on room 1.