Puzzle Dungeon: Floor 3

Question

Puzzle Dungeon Floor 3 is here!

Previous Floors: 1 2

One rule that I forgot to clarify earlier (but worth clarifying now)

A normal passage or door will not take you to a room on a later floor. Only staircases will. In addition, no room will take you up or down more than one floor, but special events may.

Without further ado, here is Floor 3 of the Puzzle Dungeon!

Items You Have:

Battleaxe (+3 Combat Power, 1 Hand)

Shield (+2 Combat Power, 1 Hand, can't use with another shield)

Sword (+1 Combat Power, 1 Hand)

20-Sided Die (+1 Combat Power)

Magic Lantern (lights up dark areas)

Book (that you can't seem to open)

Room 25

There is a passageway to room $11x$ here.

There is also a key to the locked door in room 30 here.

Room 26

There is a button labeled Not Pointless Button here.

There is a passageway back to room 32 here.

Room 27 (Start Here!)

There is a staircase up to room 15 here.

There is a passageway to room awylucreeq here.

There is a passageway to room 1, 2, 3, 5, 6, 10, 15 here.

There is a door to room N infinity here.

Room 28

There is a passageway to room enter quartet here.

There is also a passageway back to room 27 here.

Room 29

There is a button labeled Pointless Button #3 here.

There is a passageway back to room 27 here.

Room 30

There is a two-way locked door here. If you can unlock it, it leads to room 39.

There is a passageway to room odd square here.

There is a passageway to room even square here as well.

Room 31

There is a passageway to room epkywmrtdg here.

Room 32

There are passageways to every prime number room on this floor here.

Room 33

The room is covered in darkness. The lantern can reveal a passageway to room debuceerht and the words The book can be opened at the entrance of the dungeon.

Room 34

There is a zombie horde here. You need a Combat Power of 7 to defeat the horde. If you can't defeat the horde, it's GAME OVER. If you can, you move on to room earliest prime on the floor.

Room 35

There is an ancient dragon here. You need a Combat Power of 9 to kill it. If you can't, it's GAME OVER. If you can, you can head down the staircase to room $3^3*2$, next time...

Room 36

There is a warhammer here. It increases your Combat Power by 6 but you need both hands to hold it.

There is a passageway to room $x^x$ here.

Room 37

There is a suit of leather armor here. It increases your Combat Power by 1. You can't use another suit of armor with it.

There is a passageway to room two honeys hicks.

Room 38

nogzezvegitqmzhebiewlbatlsgjctlvgxamdrvhppofzuileqohcakvcihelmuvsoyewmsdxiwybvvfhqfkhigjwqcibpmeudltvfqsbvnlik

Room 39

There are 30 gold coins in this room.

Room 40

There is a magic sword here. It increases your Combat Power by 4 but you need a hand to hold it.

There is a passageway back to room owtsemitthgiesunimeerhtsemit)enosunimneetneves(.

Pointless Button #3:

A passageway opens from room 15 to room 16.

Opening The Book:

The book is mainly full of scribbles. On the last page, there is qeammdqpcfdezbdkpesbyfnlqzhuwm written in scrawled writing.

Not Pointless Button:

A passageway opens from room 1 to room 40.

Answer 1

Full (?) solution:

Starting in 27:

go to room 30, through the sequence 1,2,3,5,6,10,15 - missing value is 30 (set of factors of 30)

then:

go to room 25 (odd square on current floor), where you get a key

then:

go to room 33 (11x = 33, only possible value for this floor; likewise x^x in later room can only be 3^3 = 27)

then:

lantern reveals way to three cubed (reverse text) = 27

back to:

27, to 30, where we use the key to 39, pick up 30 gold and head back to 30 via the two-way door, then to room 36 (even square) where we get the Warhammer; back to x^x = 3^3 = 27

Thanks for the hint!

from 27:

N infinity is 28 - N rotated looks like 2, and 8 rotated looks like infinity - so on to room 28, where we are clued to the next room: Trent-quatre (34)

then:

room 34; with our new Warhammer and 20-sided die, we're able to beat the horde, allowing movement to room 29 (lowest prime on floor)

then:

room 29, where we press the button, opening a passage from 15 to 16, then back to 27, up the stairs to 15, through the passage to 16, stairs up to 7, pay the dragon (down to 20 gold now), take the passage to room 1, and open the book

the book:

using the key "ixaria" we get "I have discovered the key of lichdom", which is the key for much of the third floor.

back we go:

1 to 7 (pay the nice dragon, down to 10 gold); 7 to 16, to 15, to 27

now, in room 27 again:

awylucreeq with key 'lichdom' is power of two, which is 32 (2^5)

then:

lots of options - primes on this floor - 29, 31, 37 - let's go with 37, which gets us armour, and a path to 26 (sounds like the given phrase), where we push the button (opening 1-40), and head back to 32

then:

go back to 29, 27, 15, 16, 7 (pay with our last gold), 1, now down to 40, grab the magic sword and follow the reversed math to go to room (17-1)x 3 - 8x2 = 16x3 - 16 = 32, now to 31

in this room:

31 leads to 35 (using key 'lichdom') where I die, because my combat bonus is +4(sword), +2(shield), +1(armor), +1(die) = +8

so it's game over . . . so close . . . unless:

sword in one hand, axe in the other, armor, die = +4+3+1+1 = 9, which gets us past the dragon and on to room 54 (3^3*2)

(I also decrypted the message in room 38, but since we never get there, I'll leave it for another time...)