I’m not a data scientist, but I love these. I’ve got a four-hour flight ahead of me and a copy of Microsoft Excel; maybe now is the right time to give one a try!
!It seems like the combination of materials determines the cost of the structure.
!Architects who apprenticed with Johnson or Stamatin always produce impossible buildings; architects who apprenticed with Geisel, Penrose, or Escher NEVER do. Self-taught architects sometimes produce impossible buildings, and sometimes they do not.
!This lets us select 5 designs from our proposals which will certainly produce impossible buildings. To do better, we need to understand how to tell when a proposal by a self-taught architect is likely to produce an impossible building.
!~44% of designs by self-taught architects are impossible. This more-or-less matches the 2/5 of masters whose apprentices reliably produce impossible buildings. So I hypothesize that self-taught students pick a favorite master at random and crib their style, acting (illegibly) like a typical apprentice thereafter. So now I need to see if there are particular materials, structure types, or blueprint types which are favored by students of any of the known master architects. By choosing designs by self-taught architects which have those properties, maybe I can tease out whose style they're probably using.
!A structure can contain either dreams or nightmares, but not both.
!I'm too smooth-brained to tease out complex correlations on this flight while just using Excel: if there's something weird going on (like, buildings made with either Dreams -or- Glass are likely to be impossible, but if you use both at once they cancel one another out somehow), I don't know how to find it. So I'll just assume everything is independent of everything else and do a Bayes to it.
!We can down-select our variables to match those which appear in the Self-Taught proposals; it does us no good to learn whether the "good" architects make use of Nightmares or not, if none the proposals before us make use of Nightmares.
!Good properties: Towers; buildings of Dreams and / or Glass; Hastily-Sketched blueprints. Bad properties: Mansions, Mechanisms; buildings of wood and / or Steel; Obsessively Detailed blueprints.
!So I choose proposals D, E, G, H, and K (probability 1); and also proposal A (probability ~62%) if we've got room.
!Ok, I just got off the plane and checked the puzzle description. Turns out we only get to choose 4 buildings, and there was no reason to try and tease out what Self-Taught architects are doing. In that case, I need to rank proposals D, E, G, H, and K by likely price.
!Structure price looks vaguely exponential, so I'll take do a linear fit to minimize RMS(log10(error)). If I minimize RMSE directly then it always screws up the low-price structures to get marginally better fits on high-priced ones.
!It really looks like for each structure, you pick two materials; each material contributes a random amount to the price, with every material having its own distribution of price contributions. I can't figure out what dice or whatever are being rolled for each material, but the fit gives me the average contribution for each one.
!So I choose proposals K, E, D, and H, with expected prices 30k, 73k, 78k, and 78k. Proposal G should be impossible too, but it’ll probably cost about 572k.
This is a D&D.Sci scenario: a puzzle where players are given a dataset to analyze and an objective to pursue using information from that dataset.
Duke Arado’s obsession with physics-defying architecture has caused him to run into a small problem. His problem is not – he affirms – that his interest has in any way waned: the menagerie of fantastical buildings which dot his territories attest to this, and he treasures each new time-bending tower or non-Euclidean mansion as much as the first. Nor – he assuages – is it that he’s having trouble finding talent: while it’s true that no individual has ever managed to design more than one impossible structure, it’s also true that he scarcely goes a week without some architect arriving at his door, haunted by alien visions, begging for the resources to bring them into reality. And finally – he attests – his problem is definitely not that “his mad fixation on lunatic constructions is driving him to the brink of financial ruin”, as the townsfolk keep saying: he’ll have you know he’s recently brought an accountant in to look over his expenditures, and he’s confirmed he has the funds to keep pursuing this hobby long into his old age.
Rather, his problem is the local zoning board. Concerned citizens have come together to force him to limit new creations near populated areas, claiming they “disrupt the neighbourhood character” and “conjure eldritch music to lure our children away while we sleep”. While in previous years he was free to – and did – support any qualified architect who showed up with sufficiently strange blueprints, the Duke is now forced to be selective: at present, he has fourteen applicants waiting on his word, and only four viable building sites. He finds this particularly galling, since about half the time when an architect finishes their work, the resulting building ends up not distorting the fabric of spacetime, and instead just kind of looking weird. It’s entirely possible that if he picks at random, he’ll end up with no new impossible structures at all this month, which – he asserts – would utterly break his heart.
This is where you come in. Using his records from previous years, he wants you to evaluate his current crop of architects’ plans and pick out the four most likely to successfully defy the laws of Nature. (If there are any ties, he’d like you to resolve them in favour of whichever option is cheapest; however, his primary concern remains the instantiation of as much impossibility as possible.)
I’ll post an explanation of how I generated the dataset, and the resulting optimal strategy, sometime on Monday 20th May. I’m giving you three days, but the task shouldn’t take more than an hour; use Excel, R, Python, the malevolent mutterings of men dressed as birds, or whatever other tools you think are appropriate[1]. Let me know in the comments if you have any questions about the scenario.
If you want to investigate collaboratively and/or call your choices in advance, feel free to do so in the comments; however, please use spoiler blocks or rot13 when sharing inferences/strategies/decisions, so people intending to fly solo can look for clarifications without being spoiled.
Note: This challenge was originally commissioned by a mysterious sponsor who - after concluding their own use of it - graciously permitted me to make it public domain on the condition that I never explain who paid for it or why. In the unlikely event that you think you've seen this one somewhere before, I humbly request that you not publicly discuss this fact.
Though, to be honest, using anything more advanced than spreadsheets for this one would probably be overkill.