There once was a legendary dwarven adventurer who, after having killed all the semi-megabeasts, then all megabeasts, and all titans in the world, was given a task by the Lawspeaker of a human town that he hadn't burned yet.
"Take this map, adventurer! On it is the location of Armok's Pipe, an old, dormant volcano. Travel there, and brave it's horrors, for at the bottom you will find the greatest treasure of all, The XXAdamantine SockXX that was once worn by Armok himself!
Once you arrive, you will also need this."
The king hands the adventurer a map, and a scroll. On the scroll is a long string of numbers.
"Those numbers are said to hold the key to finding the sock. Memorize them, for if you lose them, you will never find it!"
Now, our adventurer had never been good at appraising, or bookkeeping. In fact, it was this, that had thrown him on the path of adventure in the first place. He had arrived as a migrant soapmaker, to be welcomed by the Duke.
"Oh, hello there, migrant. Soapmaker, you say? Hmm.. Well... Erm.. Ah! Our bookkeeper recently passed away due to an unfortunate accident. You don't happen to be any good at bookkeeping, are you?"
"I'm afraid not. Sorry"
"Ah well.. Perhaps you can replace our trader. He has been elected mayor, and likes adamantine, so we're not expecting him to be around much longer. You *can* do that, can you?"
"I'm afraid I'm rather horrible with numbers, sir. Hey - I'm a soapmaker"
"Hrmpf. Okay then. There's a lever 3 z-levels down that needs pulling. Could you..?"
Even though our adventurer couldn't count any further than the 9 fingers on his hands, he wasn't daft. "Pull the lever" equalled "get out of here fast" in his vocabulary. And thus he had left in a hurry, and started out on his path of adventures.
Now here he was, trying to memorize a long string of numbers written on a scroll that smelled like old plump helmets.
Failing this, he decided to tuck away the scroll between his 4th and 5th cloak, and keep it there safely.
He set off with the morning sun, and arrived at Armok's Pipe a few days later.
The entrance to the volcano was blocked off by deep chasm. At the other side stood an old dwarf, with his hand on a lever, ready to pull it.
"Hold! What is your business here?"
"I have come to seek The XXAdamantine SockXX, let me pass!"
The old dwarf pulled the lever, and a retractable bridge appeared over the chasm
"Now, please, move to the middle of the bridge, and then answer me three questions! Not one... Not two... But three questions shall I ask you! Only when you answer truthfully, will you be allowed to pass! If by any chance, you have been hexed by Armok, and are a semi-liar, please turn back and seek help in the previous riddle!"
"Uh.. Okay.."
The adventurer moved to the middle of the bridge, and the old dwarf proceeded to ask the first question.
"What is your name?"
"Urist."
"Very well. Not very original, but I sense you speak truth."
"Okay, the second question.
What is your favourite colour?"
"Lavender blush."
"You disgust me. But, very well, it seems you spoke truth again."
"Third and last: What color doth have a gibbon?"
"Erm.. Would that be a white-handed or a black-handed gibbon?"
"I dunno. Wait.. I know that one.. You're not fooling me.. Now you want me to step onto that bridge, and throw myself off, right? Begone, scum!"
With these words, the old dwarf pulls the lever again, and the bridge retracts. Urist falls down several z-levels, only to plunge into a cave river. Over his years of adventurer, he has become quite the swimmer, and so, he easily swims it upstream, into the caves below Armok's Pipe.
To his great joy and surprise, the cave river leads to a familiar sight: the entrance to the vault that holds The XXAdamantine SockXX
He opens the vault door, to find himself in a large room, with many levers neatly arranged into a long row.
Two of the room's side walls have been lined with bauxite floodgates, and the room itself is very hot.
There is a locked adamantine door. It is studded with gold. On the door is an image of The XXAdamantine SockXX in adamantine.
"So.. I guess this is what the numbers are for.. I guess I must pull the right levers, in the right order", thinks Urist.
He takes the scroll out of his cloaks.
To his horror, his detour through the cave river has managed to completely soak the scroll. Most of the ink has washed off, leaving only 6 numbers legible:
1, 3, 7, 12, 18, 26, ..., ..., ..., ...
Urist pulls the 1st lever from the row. He hears a click, but nothing else happens. The same happens when he pulls the 3d, 7th, 12th, 18th and 26th lever.
Judging to the empty spots on the paper, Urist needs to pull 4 more levers, to unlock the adamantine door.
Pulling the wrong lever will almost certainly release fiery death upon him.
What are the numbers of the 4 levers that Urist needs to pull?