The first thing to notice is that the colors of the boxes are all unique and not obvious choices for standing apart from each other, and thus are not there just for decoration. If you view the source code of the page, you can get the color of each box expressed as a hexadecimal number.
| Clue | Color |
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| There is an exit to the east, leading to a pronic room. There is also a staircase leading up. | 001FC0 |
| There is a staircase leading down to an admirable room. There is also a staircase leading up. | 015555 |
| There are exits to the east and west, and a staircase leading up. | 020AE1 |
| There is an exit to the south, leading to an automorphic room. There is also a staircase leading down. | 11EEE1 |
| There is a staircase leading up to a room that is amicable with this one. There is also a staircase leading down to an Ulam room. | 15F507 |
| There is an exit to the east, leading to a Catalan room. There is also an exit to the west, leading to a harmonic room. | 1D5AB8 |
| There is an exit to the south, leading to the smaller room of a betrothed pair. There is also an exit to the north. | 287F43 |
| There is a staircase leading up to an Eulerian room. There is also an exit to the west. | 28CF08 |
| There is a staircase leading down to a Carmichael room. There is also a staircase leading up. | 35C7E2 |
| There is a staircase leading up to a Saint-Exupery room. There is also a staircase leading down. | 3BADC8 |
| There is a staircase leading down. | 50BAF4 |
| There is a staircase leading up to a square room. There is also a staircase leading down. | 590A6F |
| There is a staircase leading up to a magnanimous room. There is also an exit to the east. | 5C56AC |
| There is a staircase leading down to a prime room. There is also a staircase leading up. | 63BCBE |
| There is an exit to the south, leading to a Moran room. There is also an exit to the north. | 6C7B00 |
| There is a staircase leading down to a perfect room. There is also a staircase leading up. | 6FFCBF |
| There is a staircase leading up from here. | 7029A3 |
| There is an exit leading south to this room’s fiancee. There is also an exit to the north. | 71D4A4 |
| There is a staircase leading up to a house room. There is also a staircase leading down. | 79757E |
| There is a staircase leading up to a Cullen room, and also a staircase leading down. | 94016A |
| There is a staircase leading up to a Perrin room, and also a staircase leading down. | 980001 |
| There is an exit to the south, leading to a tau room. There is also an exit to the north. | 998BA5 |
| There is a staircase leading down to an astonishing room. There is also an exit to the north. | 9D8000 |
| There is an exit to the east, leading to a Curzon room. There is also an exit to the west, leading to a Rhonda room. | 9F89E3 |
| There is a staircase leading down to a Fibonacci room. There is also an exit to the north. | A6B75B |
| There is an exit to the south, leading to a cube room. There is also a staircase leading down. | A761A5 |
| There is an exit to the east, leading to an anti-perfect room. There is also an exit to the west. | AA79D2 |
| There is an exit to the south, leading to a Lucas room. There is also an exit to the north. | B73E1D |
| There is a staircase leading down. | B8CA42 |
| There is a staircase leading up to a lucky room. There is also an exit to the west. | BC09A2 |
| There is an exit to the south, leading to a brilliant room. There is also an exit to the north. | C294AB |
| There is a staircase leading down to a Smith room. There is also a staircase leading up. | CB7B25 |
| There is a staircase leading down to a hungry room. There is also a staircase leading up. | D0FC21 |
| There is a staircase leading up to a primorial room, and also a staircase leading down. | EFEED8 |
| There is a staircase leading up to a Zuckerman room. There is also a staircase leading down. | F13840 |
Each box’s number has one or more properties (such as being prime, or a perfect cube, or an amicable number). For example, the last box on the puzzle page has the color #F13840, which is 15,808,576 in base 10—and a perfect square. The flavortext indicates that you don’t know where you are, which hints that you need a map. The room exits that describe the property of the room they lead to, provide enough information to create the map. All of the rooms are contained within a 5 × 5 × 5 cubical structure. Any two rooms that share a wall (or a floor/ceiling) are connected and have a door (or staircase) between them.
First (Bottom) Floor
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Color: 7029A3 7,350,691 Property: Prime Exit: U |
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Color: 5C56AC 6,051,500 Property: Harmonic Exits: E, U |
Color: 1D5AB8 1,923,768 Property: Lynch-Bell (not used) Exits: E, W |
Color: 28CF08 2,674,440 Property: Catalan Exits: W, U |
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Color: 001FC0 8,128 Property: Perfect (also Ulam, and Harmonic) Exits: E, U |
Color: AA79D2 11,172,306 Property: Pronic Exits: E, W |
Color: 020AE1 133,857 Properties: Smith Rhonda Anti-perfect (also Lucky) Exits: E, W, U |
Color: 9F89E3 10,455,523 Property: Hogben (not used) Exits: E, W |
Color: BC09A2 12,323,234 Property: Curzon Exits: W, U |
Second Floor
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Color: 63BCBE 6,536,382 Property: Admirable Exits: U, D |
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Color: 79757E 7,959,934 Property: Magnanimous Exits: U, D |
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Color: EFEED8 15,724,248 Property: Eulerian Exits: U, D |
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Color: 6FFCBF 7,339,199 Property: Hungry Exits: U, D |
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Color: CB7B25 13,335,333 Property: Astonishing Exits: U, D |
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Color: 590A6F 5,835,375 Property: Lucky Exits: U, D |
Third Floor
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Color: 015555 87,381 Property: Ulam (also Curzon) Exits: U, D |
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Color: A761A5 10,969,509 Property: House Exits: S, D |
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Color: 94016A 9,699,690 Property: Primorial Exits: U, D |
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Color: B73E1D 12,008,989 Property: Cube Exits: N, S |
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Color: C294AB 12,752,043 Property: Lucas Exits: N, S |
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Color: 998BA5 10,062,757 Property: Brilliant Exits: N, S |
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Color: D0FC21 13,696,033 Property: Carmichael Exits: U, D |
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Color: 9D8000 10,321,920 Property: Tau Exits: N, D |
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Color: F13840 15,808,576 Property: Square Exits: U, D |
Fourth Floor
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Color: 15F507 1,438,983 Property: Amicable with 1,175,265 Exits: U, D |
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Color: 980001 9,961,473 Property: Cullen Exits: U, D |
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Color: 35C7E2 3,524,578 Property: Fibonacci Exits: U, D |
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Color: 3BADC8 3,911,112 Property: Zuckerman Exits: U, D |
Fifth (Top) Floor
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Color: 11EEE1 1,175,265 Property: Amicable with 1,438,983 Exits: S, D |
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Color: B8CA42 12,110,402 Property: Perrin Exit: D |
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Color: 6C7B00 7,109,376 Property: Automorphic Exits: N, S |
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Color: 287F43 2,654,019 Property: Moran Exits: N, S |
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Color: 71D4A4 7,460,004 Property: Betrothed to 10,925,915 Exits: N, S |
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Color: A6B75B 10,925,915 Property: Betrothed to 7,460,004 Exits: N, D |
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Color: 50BAF4 5,290,740 Property: Saint-Exupery Exit: D |
Once you have mapped the cube, you need to look at the shadows it would cast if a light were shone on the entire cube from the outside; first to the north, then to the east, then down, as clued by the flavortext. If the occupied rooms (colored maroon in the image below) cast a shadow and the unoccupied rooms do not, the shadows in those directions form the letters W, A and Y, respectively—and the answer to the puzzle is WAY.
