story - Lights in the Dungeon: Four by Four

This is the second in a series Lights in the Dungeon puzzles.

_{previous (1st) <-- | --> next (3rd)}

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As you exit the three by three dungeon, you are greeted by a grinning Lord Hooty McOwlface. A grin does not make him appear friendly. Rather, you get the feeling that he's deciding which portions of you would be tastiest.

"Well!" screeches his Lordship, "Has he succeeded?"

It takes you a moment but you realize that he is not talking to you and is, in fact, addressing the purple cat sitting at a bank of computer terminals. You know this to be Fakky Jim, the Lord's grand vizier who is, by coincidence, a magic cat. He turns his furred head and utters a single, "Mreow."

"Drat!" says McOwlface. "I suppose we're on to round two, eh? Very good. The dungeon shall be larger but the rules are largely the same. Larger? Largely? I am hilarious..." He pauses for you to appreciate this but you can give nothing but a blank stare. He dismisses you with a wave. "See Fakky for the updates."

You walk over to the cat and retrieve a scroll. Unfurling it, you find the rules below (revisions from the previous challenge are in bold):

1. You will enter a dungeon in which there are many rooms. Each room has a single light in the middle. You must turn off every light.


2. The lights are easily turned off by a short chain hanging from the fixture.


3. As soon as you exit a room, the floor will collapse to reveal the thousand-foot chasm below. You may not re-enter a room and, therefore, must turn off each light by passing through each room exactly once.


4. The map below shows the current design of the dungeon with each room bordered by red and labeled with a alphabetic character.


5. You may rearrange the rooms however you like before you enter but you cannot change the overall dimensions of the dungeon. In this case, that means the dungeon must be four rooms wide and four rooms tall.


6. You cannot rotate or flip rooms. You may only translate them.


7. You may only enter the dungeon once and exit once. As soon as you exit the dungeon, any remaining floors will collapse.



8. If there are any rooms not visited and, therefore, any lights left on, you lose. If all lights are turned off when you exit the dungeon, then you win.


9. If you create a dungeon map that you cannot enter or cannot exit, you shall lose.

How can you rearrange the dungeon rooms so that you can win the game?

_{There are probably multiple solutions. The first valid answer will be accepted.}

ABBC
DDEF

GGHH
MMOO

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For reference, here are the 16 possible rooms. (Note that this is all possible rooms. For this puzzle, you must use exactly the rooms shown in the map above.)

Answer

How about:

BGBC

HFMM
OADH
OGED

This has the nice additional quality that, no matter which room you enter by, you can still complete the path.