On Doors and Passcodes, or Flying High

Question

After going to sleep one night, you wake up in the middle of a dimly-lit cavern. You can feel the cool, damp surface of the stone beneath your fingers as you push yourself to a sitting position and observe that the cavern has 10 doors, labelled 1 through 10. Each door is engraved with nine words; each door has a 10-digit keypad directly next to it. You experimentally push some buttons on the keypad. Every five number presses, a light on the keypad flashes red. Obviously, each door needs a five-digit code to open, to be determined from the nine words engraved on the door's panel.

• Door one: was thirteen when fourteen eating cookies and he nearly

• Door two: held I was were born in if raised the

• Door three: manor Jones stadium Mrs. Mr. field the of Smith

• Door four: years call Ishmael some evening we post me flour

• Door five: universally mail is a truth almost thing it fortnight

• Door six: in this among reptiles other people public buildings shiny

• Door seven: hair temple fair boy with the unfair legalism of

• Door eight: you idiot the mouse give liberation if a dapper

• Door nine: it bright cold shiny hard was a tuba master

• Door ten: he Elmer was happy drunk Gantry fine fee puzzle

Upon solving the final code, the last light flashes the welcome green, and all ten doors synchronously swing open, revealing that all ten lead to the same place - a second cavern, one with sunlight streaming in through a window. Mounted on the subterranean wall next to the window is a dust-laden beige QWERTY keyboard with a small Post-It note attached. The note reads:

You have one chance to type in the one word that can save you. Remember what got you out of the first room.

Etched in the stone beneath your feet is a number and two words:

324081: Regrind Her

After a moment's hesitation, you anxiously press what you hope are the keys to your freedom. After a few seconds of deafening silence, the window clicks open. You joyously climb out - only to wake up, and realize it was all a dream. You then decide to post the puzzle on PSE for some easy reputation.

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What were the ten numbers, and what was the word that you typed into the keyboard?

Hint One:

Surely some names on doors four and ten will trigger the minds of our literary-minded puzzlers.

Hint Two:

The word you typed in happened to be ten letters long, and for a good reason.

Answer 1

The ten five-digit numbers are

the positions, within each block of nine words, of the first five words of various books. For instance, the first one is 38192; the words are "When he was nearly thirteen", and these are the first five words of To Kill a Mockingbird.

The actual numbers, in order, are:

38192 (When he was nearly thirteen ...; To Kill a Mockingbird)
23569 (I was born in the ...; Robinson Crusoe)
52871 (Mr. Jones, of the Manor ...; Animal Farm)
28341 (Call me Ishmael. Some years ...; Moby-Dick)
83451 (It is a truth universally ...; Pride and Prejudice)
35781 (Among other public buildings in ...; Oliver Twist)
64531 (The boy with fair hair ...; Lord of the Flies)
71584 (If you give a mouse ...; If You Give a Mouse a Cookie)
16723 (It was a bright cold ...; Nineteen Eighty-Four)
26341 (Elmer Gantry was drunk. He ...; Elmer Gantry)

I confess a bit of doubt about

the eighth, which being a picture book for small children seems rather out of keeping with the other books here.

Our final word is, I take it,

TRAMPOLINE

which is

made up of the initial letters of the book titles, in order. (If 324081 has any more significance than the anagram of RED HERRING, then I regret that I missed it.)