Import Hugo

hugo/static/MysteryHunt2020/BestSongEver.nb

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hugo/static/MysteryHunt2020/Story.nb

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+    "\"\<I still remember the first time I ever visited the house. My friend \
+Emmett - from the Jazz lounge where I played sometimes Friday nights - had \
+lived there for years and invited me over for house dinner and to watch a \
+movie with him. When I arrived, he gave me a tour through the maze of rooms \
+and muralled hallways, even the treehouse out back with a drawbridge and a \
+fire pole from the third floor to the first. Just about every room in the \
+house (and there were a lot!) had a story attached to it, which made the tour \
+both really interesting and really long. When we finally heard the shouts for \
+dinnertime, I served myself the lentil curry, roasted brussels sprouts, and \
+quinoa, and wandered toward the tables. \\\"Sit over here!\\\" a guy wearing \
+an xkcd shirt called to me. I squeezed in beside him as he explained, \\\"we \
+call this the inductive table. If it can fit n people, it can fit n+1.\\\" \
+The conversation over the next half hour covered a Martian rover, raising \
+chickens, and principal ideal domains...I kind of felt like I'd known these \
+people my whole life. \\\"I wish I lived here,\\\" I said offhandedly as I \
+gathered my empty plate to wash. \\\"You totally should!\\\" said xkcd-guy \
+(whose name, it turned out, was Oliver). And I got to thinking. Much later, \
+in the darkness of a starless night as I walked home, the idea of moving in \
+seemed completely natural. I turned back to the house to see the rainbow \
+\\\"you are welcome here\\\" sign (on which someone had scrawled \\\"straight \
+people welcome on alternate Thursdays\\\") and the flower bed containing a \
+pinwheel masquerading as a pansy. I was sold.\>\"", ",", 
+     "\"\<The day I moved in, I was welcomed by a girl with lavender hair and \
+a pocket protector who gave me the unofficial tour. She pointed at a whip on \
+a hook by the door. \\\"That's in case of burglars and the like. Alice found \
+it at Goodwill along with a pair of handcuffs and a leather thong after this \
+sex dungeon went out of business.\\\" Next, she pointed at an alcove with a \
+public computer. \\\"That's to look up directions or to check facts on \
+Wikipedia if you get in an argument with someone and have to prove you're \
+right.\\\" I was entranced by the fractal screensaver that kept drawing \
+itself in exponentially multicolored smaller iterations until it was too \
+small to detect, then zoom in and keep going. The girl followed my stare. \
+\\\"Oh yeah, Ethan programmed the screensaver,\\\" she said, \\\"he could \
+keep a genius occupied for hours with math questions.\\\" As she led me up \
+the stairs, the wood floors creaked beneath our feet. \\\"It's an old house, \
+but it's totally safe,\\\" she told me. She tilted her head to the side. \
+\\\"I think,\\\" she added. \\\"And this is you!\\\" She dramatically opened \
+the door to my new room, which was super-duper tiny, but there was this prism \
+hung in the window and the late afternoon sun made shards of light dance \
+around the room. I looked at the rainbow lights hopping across the wood floor \
+and I was home. I moved the desk to the center of the room, directly below \
+the skylight in the ceiling, so I would feel like a princess in a spotlight \
+while doing psets, and plunked myself down on the chair. \\\"Seems like \
+you're all good here,\\\" she said with a smile, and it was only as she \
+turned to go that I noticed the tiny Rubik's cube earring in the loeb of her \
+left ear. Definitely at home.\>\"", ",", "\[IndentingNewLine]", 
+     "\"\<When Emmett and Savanah (also from the Jazz lounge) came to visit \
+the next week, I took them on a tour of my own through the maze of staircases \
+and rooms. \\\"This place is really cool,\\\" Savanah gushed, investigating \
+our hallway murals. \\\"It has so much charact -\\\" she stopped short and \
+stared open-mouthed at a guy dissecting an octopus and wearing exactly \
+nothing. I tugged at her elbow and led her through our common room and \
+towards our central staircase. \\\"That's Jacob,\\\" I explained. But I guess \
+that wasn't much of an explanation because she still looked like she was in \
+shock. \\\"He's course 7. He's doing his senior thesis on sea animals or \
+something.\\\" Savanah looked at me like I was crazy. \\\"But he wasn't \
+wearing anything!\\\" she exclaimed. \\\"Oh right. We're clothing-optional \
+here.\\\" She stared at me. \\\"It's really great when you forget to bring \
+your towel with you to the shower.\\\" Light from the skylight fell across \
+her skeptical face. How was it that in just a week I'd come to feel like I'd \
+lived here my whole life?\>\"", ",", 
+     "\"\<Sleep deprivation being the drug of choice in my life at the time, \
+it wasn't unusual for me to wake up disoriented with the imprint of my laptop \
+keyboard on my cheek and late afternoon sunlight streaming in through the \
+skylight above my desk. Such was my half-awake and dazed state the day I \
+walked outside and saw the pirate ship in the backyard, like a beacon \
+vertically aligned with the shed. I kind of blinked for a minute, because I \
+swear the yard was empty that morning and now there was this sailboat in it, \
+complete with a skull-and-crossbones flag. \\\"Ahoy matey!\\\" Oliver called \
+to me as he took a running start, leapt into the boat, and struck a pose. \
+\\\"Ahoy?\\\" I called back, a little confused by where this was going with \
+no water. The compass he held in his hand glinted in the sun. \\\"What's a \
+pirate's favorite mathematical field?\\\" he asked me. I stared at him. \
+\\\"Arrrr!\\\" called Ethan as he hurdled himself from \
+I'm-not-even-sure-where into the boat and gave Oliver a high five.\>\"", ",", 
+     "\[IndentingNewLine]", 
+     "\"\<By the end of the day, the boat, which Oliver had completely fixed \
+up from an old crumbling dinghy, was ready for its big debut in open water. \
+We got it loaded onto a makeshift cart-thingy and about a dozen of us walked \
+it down to the river for moonlight sail. Ethan and Oliver eased it into the \
+water and hopped on board, while the rest of us split into twos and threes \
+and boarded other sailboats at the dock. Soon we were all out on the river, \
+gliding peacefully through the crisp night air and gazing at Orion in the \
+southeastern skies. That is, until Alice and Jacob slid in close to Ethan and \
+Oliver and splashed them with a bucket of river water. Within minutes, all \
+five of our boats were in a water war, each of us attempting to get close \
+enough to another to throw water at one another and then sail quickly away. \
+We were all relatively evenly matched and relatively evenly soaked until the \
+pirate ship started pirating. Ryan and I watched it coming towards us and \
+prepared our bucket for attack. But just as it got within feet of our boat, \
+and before we could even lift the bucket, Ethan leapt off his vessel and \
+landed beside me. He grabbed hold of the sail of our boat with each hand and \
+leaned back with all his weight. Within moments I was in the river, coughing \
+and spluttering and looking around for our capsized dinghy. It only took me a \
+few seconds to locate it and swim towards it, and as I grabbed hold of the \
+side and began trying to right it with Ryan's help, I saw a dripping wet \
+Ethan grinning and waving at us beneath his black flag as he sailed away. My \
+teeth were chattering when we all walked home together about an hour later, \
+and I was desperately looking forward to the toastie warmth of home and a \
+promised fire in the fireplace. The rainbow sign on the door could not have \
+come soon enough. By the time I was dry and changed into fresh clothes, the \
+fire was crackling and half a dozen people gathered around it singing. I \
+joined in \\\"Maxwell's Silver Hammer\\\", warmed by the music of this cozy \
+little group gathered in the darkness lit only by the twisting flames. \
+\\\"Anyone want cookies?\\\" Amy asked as she came in from the kitchen with a \
+heavenly smelling tray, and my evening was complete.\>\"", ",", 
+     "\[IndentingNewLine]", 
+     "\"\<Despite all the warm-fuzzies of the fireplace and singing and \
+kumbaya and all that, Ethan was not off the hook. Oh no. I mean, it was all \
+in good fun, and yeah it was a pretty badass move, but Ryan and I knew we had \
+to plot a comeback. The idea came to me when Ryan sent out an email asking \
+all the cooks to send him their menus, since he was in charge of the shopping \
+(usually he tried to do his house job as early as possible in the week, but \
+he'd been hosed.) See, I knew that while Ethan loved broccoli and cauliflower \
+for their repetitive geometry, he hated tropical fruit. So I just suggested \
+we replace at least one requested item from each day's menu with a tropical \
+fruit as a little surprise. I figured the cooks would be totally down to \
+experiment with how to incorporate an unexpected ingredient...and I happen to \
+love papaya. By the time the last menu came in that evening, we only had \
+about a half hour before the grocery store closed for the night and in the \
+rush to go, I tripped over the flower bed outside the front door. By the time \
+we had scooped the soil back in, we had twenty minutes left. We literally ran \
+to the store, breathlessly grabbed a cart, and practically sailed through the \
+maze of aisles, trying to find each one of the dozens of items listed, not \
+always very helpfully (like seriously, somebody had written \\\"granola from \
+a brand that's called nature something or maybe something nature and I think \
+the package is red but it might be green\\\"). Anyway, by 10:59 our mission \
+was accomplished: all weekly food had been bought plus two bags of fruit. The \
+next day, Priya looked at the twenty mangoes we had bought her instead of her \
+requested bell peppers, read the note we had enclosed with it, and laughed. \
+We all enjoyed the mango pilaf that night...except Ethan. But the best part \
+was the look on his face when he tried the dragon fruit pudding (and the rush \
+he was in to rinse his mouth after he spit it out). Priceless.\>\"", ",", 
+     "\[IndentingNewLine]", 
+     "\"\<Ethan prepared his response that night. He crept out to the back \
+yard in the darkness with a pineapple in tow. He had decorated it to look \
+like a face with wild carrot-spirals for hair and a superman cape. He placed \
+his artwork at the end of the bow with a sign that said, \\\"I may not be \
+delicious but I am the captain of the pirate ship and I contain the Fibonacci \
+sequence. Mwahahaha.\\\"\>\"", ",", "\[IndentingNewLine]", 
+     "\"\<I noticed Captain Pineapple the following morning as I went out for \
+a run. Several of my housemates were already outside doing pushups and \
+sweating profusely. \\\"We're doing the Murph,\\\" Amanda gasped as she \
+rested for a moment. \\\"It's a CrossFit workout...next exercise is 300 \
+squats; want to join?\\\" she asked, with a can-do attitude. I watched Carlos \
+collapse into the grass and roll onto his back. \\\"I'm good,\\\" I said and \
+took off toward the Esplanade. The rush of blood felt good throughout my body \
+after a long week of psets and the early morning world seemed exceptionally \
+alive. I watched the T glide across the Longfellow bridge like a caterpillar \
+on ice skates and thought about all the people inside going places, thinking \
+thoughts, experiencing experiences...it just kind of suddenly felt like I was \
+this simultaneously insignificant and all-consuming being, like everything I \
+did and said was the entirety of my own life but it was all a speck of dust \
+in the world at large. I gazed at the sparkling river in the morning sunlight \
+that just days ago I had fallen into in the darkness of night, and I planned \
+my next move. As soon as I got home, I went to the fridge and took out all \
+the dragon fruit left over from the pudding. I cut it up and arranged the \
+pieces on the seat of the boat, forming the word, \\\"truce?\\\"\>\"", ",", 
+     "\[IndentingNewLine]", 
+     "\"\<After that, the pirate ship moved to the shed. In the years to \
+follow, it would go on many more journeys, but this is the tale we still tell \
+first to curious visitors. I had a professor that semester that always used \
+to say, \\\"this isn't fun-and-games topology; this is point-set \
+topology!\\\" And I guess I could say the same thing about that house. I mean \
+sure, it was fun, and sure there were games, but it wasn't just fun-and-games \
+coop life, and over time I would discover layers of depth in this group of \
+people that I hadn't noticed on first meeting. My housemates were the compass \
+that got me through each day that year. And sure, it was kind of annoying to \
+find that the Coke someone had left open on the side counter was still there \
+and still open 10 days later. And then to discover a lightened ring in the \
+wood of the countertop 14 days after that, and the Coke still there and still \
+open. And then to discover 9 days after that that was an intentional \
+experiment, not to see if it would grow mold (which it did!) but to see if \
+someone would take the initiative to throw it away (which obviously no one \
+did, but honestly we were just trying to be respectful of someone else's \
+drink/experiment!). And yeah, it's kind of fun to take a break at 3am from my \
+automorphic forms project and hear someone tell the story of the superman \
+Fibonacci fruit (and have someone else argue that it wasn't superman \
+Fibonacci fruit, it was electric bluegaloo Fibonacci fruit). But it wasn't \
+just about the games and it wasn't just about the pranks. It was about living \
+a life worth living with people worth living it with. And peace and love and \
+all that hippie stuff. So yeah, that's my story. The end.\>\""}], 
+    "\[IndentingNewLine]", "}"}]}], ";"}]], "Input",
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+Cell["\<\
+And lots more data, this time from the page\[CloseCurlyQuote]s source (not \
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+\>", "Text",
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+859867553894174416504787828421836027199486\>\"", ",", "\"\<\\n\>\""}], 
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+Cell["\<\
+The numbers have useful binary expansions: there are exactly as many bits in \
+each number as there are characters in the corresponding paragraph.\
+\>", "Text",
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+Cell["\<\
+There turn out to be very few 0 bits in those numbers, and they indicate \
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+\>", "Text",
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+}
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+*)
+

hugo/static/MysteryHunt2020/Z3Interop.wl

@@ -0,0 +1,98 @@
+(* ::Package:: *)
+
+BeginPackage["Z3Interop`"]
+
+
+Assertion::usage="Assertion[condition] is a symbolic representation of the assertion that the given condition holds.";
+Declare::usage="Declare[var_Symbol, Integer] is a symbolic representation of the integer variable named var.";
+CheckSat::usage="CheckSat is a symbolic representation of the command to check satisfiability at the current point in the model specification.";
+GetModel::usage="GetModel is a symbolic representation of the command to print out a satisfying model.";
+
+getDefinitions::usage="getDefinitions extracts the integer variables from a Z3 output and converts them into Wolfram Language expressions."
+toString::usage="toString[symbols_, expr] converts a line of Z3 program (given as a specification either as a Wolfram Language expression or in terms of Z3Interop primitives) into a string.";
+
+
+Begin["`Private`"]
+
+
+toString[symbols_, Equal[i_,j_]]:=StringJoin["(= ",toString[symbols, i]," ",toString[symbols,j],")"]
+toString[symbols_, Greater[i_,j_]]:=StringJoin["(> ",toString[symbols,i]," ",toString[symbols,j],")"]
+toString[symbols_, Less[i_,j_]]:=StringJoin["(< ",toString[symbols,i]," ",toString[symbols,j],")"]
+toString[symbols_, GreaterEqual[i_,j_]]:=StringJoin["(>= ",toString[symbols,i]," ",toString[symbols,j],")"]
+toString[symbols_, LessEqual[i_,j_]]:=StringJoin["(<= ",toString[symbols,i]," ",toString[symbols,j],")"]
+toString[symbols_, Or[a_,b_]]:=StringJoin["(or ",toString[symbols,a]," ",toString[symbols,b],")"]
+toString[symbols_, Xor[a_,b_]]:=StringJoin["(xor ",toString[symbols,a]," ",toString[symbols,b],")"]
+toString[symbols_, And[a_,b_]]:=StringJoin["(and ",toString[symbols,a]," ",toString[symbols,b],")"]
+toString[symbols_, Not[a_]]:=StringJoin["(not ", toString[symbols,a], ")"]
+toString[symbols_, Unequal[a_, b_]]:=StringJoin["(not ",toString[symbols,a==b],")"]
+toString[symbols_, i_Integer]:=ToString[i]
+toString[symbols_, a_+b_]:=StringJoin["(+ ",toString[a]," ",toString[b],")"]
+toString[symbols_, Integer]="Int";
+toString[symbols_, Declare[var_,type_]]:=StringJoin["(declare-fun ",toString[symbols,var]," () ",toString[symbols,type],")"]
+toString[symbols_, Assertion[expr_]]:=StringJoin["(assert ",toString[symbols,expr],")"]
+toString[symbols_, CheckSat]:="(check-sat)"
+toString[symbols_, GetModel]:="(get-model)"
+toString[symbols_, h_[tail___]] /; MemberQ[First/@symbols,h]:=StringJoin[h/.symbols, "_", Riffle[toString[symbols, #]&/@{tail},"_"]]
+
+
+r=RegularExpression["\\(define-fun (.+?) \\(\\) Int\\s+([0-9]*)\\)"];
+getDefinitions[symbols_, output_]:=(First[#][Sequence@@(FromDigits[#,10]&/@Most[Rest[#]])]->FromDigits@Last[#])&/@(MapAt[#/.(Reverse/@symbols)&,StringSplit[#,"_"],1]&/@StringCases[StringReplace[output,"\n"->""],r->"$1_$2"]);
+
+
+End[]
+
+
+Protect[Assertion];
+Protect[Declare];
+Protect[CheckSat];
+Protect[GetModel];
+
+
+Begin["`Nonogram`"]
+
+
+gapsToConstraints::usage="gapsToConstraints[column_List, columnIndex_Integer, totalNumberOfRows_Integer, variableHead_Symbol] converts the data from the given column (which is column number `columnIndex`) into a set of constraints on that column (without reference to any rows). The same is true interchanging the notion of 'row' and 'column'.";
+constrainedCells::usage="constrainedCells[rowGap_Symbol, colGap_Symbol, cellVariable_Symbol, rows_, cols_, constraintsFromRows_, constraintsFromCols_,colourMapping_] uses the data from `gapsToConstraints` applied to the rows and columns, and produces the additional constraint which tie the rows and columns together. The output omits the original input constraints. `rows` and `cols` should be the actual data of the shape {{{index, colour}, {index, colour}}}.";
+
+
+Begin["`Private`"]
+
+
+Z3Interop`Nonogram`gapsToConstraints[column_,colNum_Integer,totalRows_Integer,variable_Symbol]:=
+With[{lhs=MapIndexed[variable[colNum,First@#2]+First@#1&,column]},
+With[{rhs=Append[variable[colNum,#+1]&/@Most@Range[Length@lhs],totalRows+1]},
+With[{operations=Append[If[#[[1]]===#[[2]],Less,LessEqual]&/@Partition[Last/@column,2,1],LessEqual]},
+With[{middle=#[[1]][#[[2]],#[[3]]]&/@Transpose[{operations,lhs,rhs}]},
+Join[{1<=variable[colNum,1]},middle]]]]]
+
+
+Z3Interop`Nonogram`constrainedCells[rowGap_Symbol, colGap_Symbol, cell_Symbol, rowsIn_, colsIn_, constrainedRows_, constrainedColumns_,mapping_] :=
+Join[
+(* Constraints on the rows *)
+Flatten[Table[
+Xor@@Prepend[
+(rowGap[row,#]<=col&&col<rowGap[row,#]+rowsIn[[row,#,1]] && cell[row,col]==rowsIn[[row,#,2]])&/@Range[Length@constrainedRows[[row]]-1],
+And@@Prepend[rowGap[row,#]>col||col>=rowGap[row,#]+rowsIn[[row,#,1]] &/@Range[Length@constrainedRows[[row]]-1],cell[row,col]==White]
+],
+{row,1,Length@rowsIn},{col,1,Length@colsIn}],1],
+(* Constraints on the columns *)
+Flatten[Table[
+Xor@@Prepend[
+(colGap[col,#]<=row&&row<colGap[col,#]+colsIn[[col,#,1]] && cell[row,col]==colsIn[[col,#,2]])&/@Range[Length@constrainedColumns[[col]]-1],
+And@@Prepend[colGap[col,#]>row||row>=colGap[col,#]+colsIn[[col,#,1]] &/@Range[Length@constrainedColumns[[col]]-1],cell[row,col]==White]
+],
+{row,1,Length@rowsIn},{col,1,Length@colsIn}],1]
+]/.mapping;
+
+
+End[]
+
+
+Protect[gapsToConstraints];
+Protect[constrainedCells];
+
+
+End[]
+
+
+EndPackage[]