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A Collection of DROD Riddles (By Wesley Chua)
Beethro entered a room of King Dungan's dungeon. He had realised that this dungeon was far larger and more dangerous than he had anticipated and decided he would need much more pay than he stated on the contract, if he managed to finish the job. He had found a very large sack in a corner of the previous room and was intending to collect in it the most gruesome parts of the enemies in his opinion; their eyes and legs, for explaining to King Dugan if he did not understand the true horribleness of his problem. When Beethro looked round the room, it seemed as if none of the enemies had seen him. Far above, the full moon was covering the castle in a white sheen, and below, all the enemies were asleep, and no enemies were spawning. He then proceeded to exterminate the pests quietly, and at the end found he had collected 76 eyes, 32 legs and had killed 73 monsters altogether. It was night, and Beethro was tired, so he could not remember what monsters he had killed and how many of each there were. He knew that there were no spiders in this room, as the floor did not disguise them well here and no tar of any sort at all. He also knew that there were no wraithwings on the ceiling, that he was not on the lowest floor, and that everything he stabbed died. He thought for quite a while, but the only things he could remember were:
* If there had been twice the number of roach queens, there would have been the same number of enemies as the number of eyes in his sack right now.
* The number of goblins he had killed multiplied by the number of goblin legs in his sack equalled the total number of legs in it right now.
* The number of roach queens he had killed multiplied by the number of goblins he had destroyed was equal to the number of roach eyes multiplied by the number of roach queen eyes in his sack.
* Roaches and roach queens have 2 eyes and 6 legs, Wraithwings have 2 eyes and 2 legs, Serpents have no legs, but 2 eyes, Evil eyes have one eye, but no legs, Tar needs no legs, but babies and mothers have two eyes, Spiders have 2 eyes and 8 legs, Goblins have 2 eyes and legs, and Brains have neither.
Tired out from all this thinking (from where the thoughts came from, he had no idea), Beethro decided to move on; it wasn't important anyway, as the bloody mess of eyes and legs would make a big enough impression on the King, he thought. Groping in the dim light for his map, he found he had not got it with him, and realised he was lost. He set off in search of it and took with him his heavy sack.
Can you help Beethro by finding out how many of which monsters Beethro killed, and in which room he was?
Beethro was clearing his way through Dugan's Dungeon at a relatively fast rate. He had left a room he had just conquered, and on the moment he entered another, a voice suddenly boomed out from nowhere. It said:
"Stop! Don't make a move! Your silly quest to clean this dungeon out is now over because I know where you are right now. You had better leave this instant before I destroy you!"
Beethro, startled, froze for a minute as he listened to the voice. Then, recollecting his courage and wits, he called out: "Who are you?"
"I'm the ruler of this dungeon and all its inhabitants and controller of everything that goes on in here, and I deem you as an intruder, for you are killing my subjects and causing havoc to my defences. If I were you I'd better leave right now!"
Beethro replied: "I've got a contract to the king to clear out all this vermin and to get everything cleaed up. You'll be on my list too if you caused all of this mess!"
The voice laughed, a chilling and cold laugh, then went on: "You are a fool to defy the Neather, king of this dungeon, for I hold great powers and am about to destroy your puny life, Beethro!"
The voice laughed again. Beethro, a little bit worried thought of a plan, and called out again.
"What do you intend to kill me with, then?" He said.
"I've got one mimic potion with me, and I can place it anywhere I like." He replied.
Beethro smiled, sat down and relaxed. "Go ahead then!" He called. "Try and kill me with your mimic because I know you can't."
The voice became irritated. "I shall, if you annoy me any more", it shouted. "My mimic is and does everything exactly like yours, so there is no way you can escape from me. This is your last warning from me to leave, so you'd better do it right now."
Beethro, nevertheless, ignored the voice and began to daydream. The Neather got so annoyed that he actually tried to place the mimic so that it would stab Beethro, but to no avail. He then placed it on the floor of the room and tried to move the mimic around in all sorts of ways to get Beethro, but still to no avail. Eventually, the mimic, being exhausted, simply fell apart, left the Neather fuming mad because he had not got another, and let Beethro continue his job.
In which room(s) must Beethro have been in (First Caravel DROD 1.5 release)?
"The Study Of The Dungeon (Part 2)"
All at once, Beethro heard a voice in his mind saying, "72 different killing moves. The answer is 72." (Thanks to Ferday who found the correct answer)
Beethro realised that the voice was talking to him and giving him the answer to his nephew's problem.
"72," he repeated, "72."
"Are you sure?" asked the nephew.
"Of course," Beethro replied, though he himself was not sure if the answer was correct or not.
"Ok, that's great! See you later Uncle Beethro!" called his nephew as Beethro continued along the road.
"The Study of the Dungeon and Its Inhabitants?," thought Beethro as he walked. "What utter rubbish!"
A short while later, he came to the field at exactly noon. However, his astonishment at what he saw on the field was so great that he could not do anything but stare. The field had been turned into some sort of giant research project; countless numbers of large objects had been brought to the field, along with around a thousand people, all of which were moving objects or arranging them in set-ups, or recording some sort of data. The field was a riot of movement, colour and noise.
Beethro was truly shocked by the scale of the event, for this was the largest he had ever seen in his whole life. A man ran up to Beethro, who was still absorbed in his amazement, and said, "Please, sir, could you move away from this area because we are going to set up here? Thank you."
Beethro replied, "What is all this? What are you doing here?"
"We are on contract from King Dugan," replied the man. "We have been given the task to do research into the number of room arrangements there are, as part of King Dugan's new research project: 'The Study of the Dungeon and Its Inhabitants'."
"I can't believe it! Is the king that serious about this new 'Study of the Dungeon' project of his?" exclaimed Beethro. "Why does he want to go to the bother of doing all this? What's the point?"
"We don't know. All we do now is that our boss signed a contract with the King, and so we have now ended up doing this job, on pain of a giant fine or being thrown to the roaches in the mountains if we fail."
Beethro was now curious about what was going on.
"Can you show me round the site?" he asked the man. "I've never seen such a large event before like this, and I'm just curious about it. I hope I'm not disturbing you."
"Of course not!" the man replied. "We've already shown quite a number of inquisitive people like yourself around. Follow me,"
Beethro followed. The man first took him to a small platform with four squares marked on it in a 2x2 arrangement.
"Why is this platform just grey? I always thought dungeon floors come in two colours, not one," Beethro said.
"We pleaded with Dugan and persuaded him that having two colours would make the task too confusing, so he let us off and allowed us to just have a single coloured floor," the man replied.
He took Beethro towards a large group of piles of the objects that were positioned nearby. Beethro at once ran forward towards them when he saw what the objects actually were. Grabbing them and admiring them one after another, he exclaimed: "This model force arrow is so realistic! And this potion looks exactly like the ones I used down in Dugan’s Dungeon. Everything that I saw down there you have here now in models, even monsters! How did you do it?"
“Yes. If only we ourselves could also admire and experiment with them like you are doing, but we can’t, since we don't have the time. Today is Novender 37, 147 B.D., and King Dugan wants us to finish by 13 Onsuary next year, which gives us only two weeks."
"What is this problem?" Beethro asked.
"Using all the elements you can find in a dungeon, combined in every possible way, find out how many theoretically possible arrangements of these that there are in a 2x2 DROD room," replied the man. "What this means is that we are to take every element that can be found in a dungeon (Caravel DROD release 1.6), such as walls, floors, gates, monsters and pits, and any other possible combinations of these, such as a roach on top of a force arrow, or a goblin on a trapdoor, and find the total number of all theoretical arrangements of these in a room."
"Do rotations and reflections of arrangements count?" asked Beethro.
"Yes," said the man. "The orientation of an object is also important. A roach facing north is considered different from a roach facing south, for example."
Beethro then had a thought. He began to search the piles for a particular object that he had noticed was not present.
"What are you looking for?" inquired the man.
"Do you have a model of the 'Neather?" asked Beethro.
"Err... no. What is a 'Neather?"
Beethro then realised that the 'Neather was a secret that probably only he out of all the dungeon exterminators knew about, and that he had to keep it secret, just in case the DAA (Dungeon Architects' Association) discovered he knew about it. He replied cautiously, "I don't know myself. I once heard a rumour about a monster called a 'Neather, and was curious to see if it existed. You don't have a model of it, so it can't possibly have."
Beethro then turned to the people working on setting up the arrangement. Suddenly, one of the supervisors pointed at the platform and shouted, "No! That arrangement has never been allowed! Orbs cannot exist on trapdoors. Architects have designed orbs to have a special structure that prevents the rock that they are placed on from ever crumbling or collapsing. You should know that!"
The worker immediately corrected the problem, and the work then continued.
Beethro then attempted to think about the puzzle himself, but soon realised that the number was going to be far larger than he could possibly comprehend. He turned to the man and said, "It would take me years to work all of them out. I don’t think I could possibly help at all."
"We’ve already completed about 300 different arrangements," said the man in reply, "but indications seem to show there are probably thousands of arrangements. At 2 minutes to set up each arragement, even working around the clock without stopping, we couldn't possibly find them all in just 2 weeks, since we need to set up each arrangement and record it before we set up the next. There has to be an easier way to do it, or we are going to fail for sure. Do you have any idea about what we could do?"
Can you help the poor researchers solve the problem given to them by the King, and find out how long their method would take to make all of the different arrangements?