### by Catherine Wu

### Answer:

NIGHTMARE

In the puzzle, we have rooms and hallways presented from different vantage points. The first step is to piece together the images using shared features to draw an overall layout. We can’t assume that, for example, all poles are the same, but it is useful to note that the outside of a building is typically white.

Feature | Images |

Checkerboard floor (with windows and pole) | |

3 poles | |

Banister / Diagonal hallway | |

Banister (straight hallway) | |

Trapdoor | |

Stairs 1 | |

Stairs 2 | |

Short hallway with half-wall | |

Skylights | |

Pole 1 (diagonal hallway) | |

Pole 1 (third floor view) | |

Pole 2 (ceiling light, hole) | |

Pole 2 (hole, grate and trapdoor) | |

Free ladder and hall behind it | |

Hall (147 cube, ceiling light, arch) | |

We can also see three distinct cubes that appear to have the dots 1-9 labeled on three faces each. (We can only see 1-8; the 9 must be inferred.) As we piece things together, we eventually realize that these are in fact three separate buildings that have been mixed together. We can separate the features above into three disjoint sets of pictures, lumping together features when they both appear in a single picture. Each building has one of the cubes, which gives the order for these buildings.

### Building 1

- Checkerboard floor (with windows and pole)
- Banister / Diagonal hallway
- Pole 1 (diagonal hallway)
- Pole 1 (third floor view)
- Hall (147 cube, ceiling light, arch)

### Building 2

- Trapdoor
- Stairs 1
- Pole 2 (ceiling light, hole)
- Pole 2 (hole, grate and trapdoor)

### Building 3

- 3 poles
- Banister (straight hallway)
- Stairs 2
- Short hallway with half-wall
- Skylights
- Free ladder and hall behind it

We want to use the weird layouts of the building. If we look at the building from the direction of each of the dice faces, the projection corresponds to a letter. Taking all 9 letters in this way, assuming the floor to be the bottom and consistent perspective for each building, we get the answer **NIGHTMARE**.

| Building 1 | Building 2 | Building 3 |
---|

Top | | | |

Left | | | |

Right | | | |

The sketchup files used to create these images can be found here.

## Authors' Notes

Thanks to Eli Cohen, Kai Eubanks, and my unread copy of *Gödel, Escher, Bach* for the inspiration.