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This quest was originally ran during the 2020 anniversary - here. After nearly a year, I happened to discuss this quest with @Aia del Mana, who had generously offered to sponsor this into a permanent quest. In essence, the quest is identical, though, after it has proven to be of... quite high difficulty, the requirements has been reduced somewhat, and the rewards increased to reflect it. The quest will be, as following: A hunt for Darvin. Darvin, the advanced Aramor, had escaped into a new section of the labyrinth, and needs to be captured. This new section is a huge interconnected area, akin to a chessboard. Each turn, A25 holders, using their given A25 tools, freely teleports into a tile of their choosing. Each turn, Darvin surfs the heat current, moving to a different adjacent tile. He cannot move to tiles diagonal to his current location, as there would be no heatvein connecting the two square. He cannot remain still, as such is the nature that he was given. Each party action happen simultaneously. The tool holders and Darvin must move, at the same turn, to the same square, for Darvin to be considered "found". By chance, magic, or unknown mechanic within the realm itself, almost like quantum physics, he cannot be found unless, by deduction, he must be found. Should one seek him out at random, even how improbable it would be, he shall never be found. Noticing these rules, Chew deducted a simple way method: to organize a massive manhunt, placing players in every tile. Gets the job done, gets it done fast. However, Mur insist that the A25 tools may only be handed out to as few people as possible. To this end, find the methods needed, and the numbers of tools to hand out, to solve the following situations: 1. If the labyrinth size is 3x3. For this simple case, simply pointing out a correct pattern (with the minimum number of tools holders), would suffice. Those who solve this should expect a spell document to celebrate their success. 2. If the labyrinth size is 5x5. A detailed mathematical proof, showing not only the pattern, but that it is indeed the minimum number of tool holder needed. A wishpoint will be rewarded. 3. If the labyrinth size is unknown (n x n). A detailed mathematical proof, showing the pattern/rules is required. A single selection between a colored Winderwild, Elemental, or Pope, shall be rewarded. This is not first-come, first-served, anyone who managed to meet the requirements shall be rewarded all the same. I could provide aid and discussion if you want to challenge this - as this task is quite difficult. In mathematical terms (or simplified terms): Darvin will be on a chessboard-like grid. Each turn, he must move one tile, up, down, left or right. Each turn, you choose a number of squares to find Darvin. Actions happen simultaneously. Darvin is considered found, if he and you chose the same square. Darvin cannot be found at random. You must prove that he must be found using your pattern. Think of it as a strategy game, and that he knows your strategy from the very start. Find a pattern that he can't beat. You must find a pattern that requires the least amount of searches per turn. 1. Find the solution if the square is 3x3. No proof required, just the pattern. I've been authorized to grant you a spell-document should you submit a valid solution. 2. Find the solution if the square is 5x5. Proof, including why the pattern is optimal (uses the least amount of searches per turn), is required. A wishpoint will be rewarded. 3. Find the general solution for an n x n square, showing the pattern, as well as the proof for why it is optimal. Aid may be provided if requested. You may choose between a colored Winderwild, Elemental, or Pope as your reward. Rules: Solutions must be submitted in a private manner. Any private methods is acceptable, though I must warn that I do not check the ingame inbox often. Do not discuss, share, or collaborate. Please check your work thoroughly before submitting. If I feel like you're probing for the answer by having me pointing out mistakes, you may be disqualified. This applies mostly to reward 1, and somewhat for reward 2. To clarify, for task 2 and 3, a detailed proof of not only how the pattern will work, but also why you can't find Darvin with less tool holders will be required. For task 1, simply showing a pattern would suffice, without much explanation needed. If there's anything you need clarification on, feel free to DM or post a reply. Winners: Tier 1: @Aelis(as he finished it during the 2020 anniversary) @Kaya- May 7th, 2021 Tier 2: @Kaya- May 10th, 2021 Tier 3:
The other day, I headed to the Golemus Laboratory, for some experimentation. Tinkering around, messing with the Aramors to-be-filled with AI cores. Alas, such work is boring! So boring indeed, that half way through, as my attention span dictate... I decided to make a very, very bouncy ball. A drop of blood, glue, rare minerals... and Voila! Throwing this thing in open space, would be unwise. Not that it would do any damages, but I prefer to not lose my shiny possessions. So, I had a small room built, and gave it a throw. Alas... I did not expect it to bounce so vigorously, the damn thing bounced so well, catching it would be impossible! As I ponder upon this dilemma, miraculously, the ball bounced straight back at me. Damn thing almost broke a tooth of mine, but I did managed to catch it. Impressed by this outcome, I laid down my pen and paper, and begins working out, how exactly did the ball bounce back to exactly where I was? And how many times, did that damn thing bounced around? So, I ask for your help, to determine the numbers of bounces the ball made. Here are the details of how it all went down - according to my memory: The ball somehow ignored gravity, and flew parallel to the ground at all times I started at the South-West corner of the room The ball was thrown perfectly North-East. (45 degree) The room is almost a square, of dimension 2020 cm x 2021 cm. I fully intend to sue the contractor for this error. Summarized in mathematical terms: You throw a perfectly bouncy ball in a rectangle (2020 x 2021) room from a corner The ball was thrown at a 45 degree angle The ball ignored gravity, and flew parallel to the ground at all time How many bounces did the ball make before it return to your location? Rewards: Most elegant solution - 1 Anni crit Most creative/unorthodox solution - 1 Anni crit Fastest correct solution - 1 GC All correct solutions - 5SC + 1 spell stone Lock in chaos Acoustic Remains Teleport to Papercabin
Just recently, I passed by the Tempest Fort, and noticed a worrying issue. Moss! Some strange moss had invaded the walls. Its root penetrated the solid stone, and weakened its integrity! Unacceptable! However, it seems that the stones available to patch up the walls is in short supply, and on top of that, they naturally form in difficult shapes. Thus, I'd like to employ your help, to find a way, to most efficiently replace the damaged walls. The wall to be replaced could be modeled as a solid slate, of dimensions 8x8x3. There are various types of stones available: Z, T and L shaped stones (volume of 4) I shaped stones (volume of 2, or 1x2) Singular, dot/square ( . ) shape stones, volume of 1 Your goal is to find a way to assemble the 8x8x3 walls using these materials. In general, based on scarcity of materials, I've assigned the tiles the following points: Z shape: 4 points T and L: 3 points I: 1 points dot: 0 points The winning designs shall be rewarded handsomely. In particular: The design with the highest score shall win 3 gold coins, and an anni creature The second place, would be 2 gold coins, along with an anni creature The third place, would be receiving 1 gold coin, and an anni creature However, there's more! I look not only for the design that has high point values. There's more to this challenge, than simply finding a single solution with a good point value. Artistry and beauty is a major aspect of masonry. I look also for designs that amazes me, regardless of how well they perform in the actual competition. In particular: Designs with a certain mathematical "beauty" - whenever that be an absolute order, scalability, or an extremely chaotic, complex yet efficient pattern Designs with fantastic demonstration and illustration, demonstrating a huge amount of effort & care Etc. In general, anything that amazes me greatly, would be rewarded with 1 WP. Your design does not need to achieve a high score to a WP, but a high score itself could certainly amazes me. There's no limited to how many winners, but there's no guarantee that there would be a winner as well. Deadlines and submission guidelines: Deadline: You have until the end of anniversary (29th) to submit your design Submission guideline: You can submit your design in any manner that you like. Rather, coming up with a unique design AND presentation is part of the quest, at least for the WP portion For clarity, I'd ask that you make three 8x8 squares and fill it with numbers. Squares with the same number should be occupied by the same "stone". You may also submit just this three squares as your submission. Below are the shapes, in image form (with a thickness of 1), as I've been notified that there are confusions to the shapes. They're somewhat similar to tetris shape, as you can tell.