# Solution to Green Building

#### by Nathan Pinsker and Brian Chen

```LIZ CLAIBORNE
VIEWTIFUL JOE
ESCAPE VELOCITY
CAPTAIN HOOK
ELECTRIC LIGHT
ALL-SEEING
LUMINESCENT
LJUBLJANA
ROMEO AND JULIET
INTELLIGENCE
STATE LINE
ARMIN ZOGGELER
NONCONFORMIST
```

This is the metapuzzle for the Green Building. We’re presented with a 13×5 grid of windows, with trees on either side of the bottom row. Furthermore, solving a puzzle in the round unlocks a switch corresponding to the next highest floor.

The switch can be toggled on and off, and turning it on lights up some windows on the building itself. If we decode the bottom row as five bit binary in order of the floors we spell FAMOUS MIT HACK.

One of the most famous Green Building hacks involved turning the building into a playable tetris game by lighting up the windows on the building’s northern face. A natural thing to do then would be to interpret our lighted-up grid as a Tetris grid.

Every meta answer contains some of the letters I, L, J, S, O, Z, T, corresponding to the seven possible Tetris pieces. By removing all the other letters, we can turn each answer into a sequence of tetris pieces. For each lighted-up board, we can identify an answer whose sequence of Tetris pieces clears the board when the pieces are dropped at the appropriate positions.

For example, the following board, corresponding to switch #1, is cleared with CAPTAIN HOOK. Removing all non-Tetris letters gives the sequence TIOO.

Each board can be uniquely cleared with a sequence of Tetris pieces obtained from an answer. Matching the answers to the boards is a little tricky, but there are a few heuristics we can use to make things easier. For example, the board corresponding to switch #1 initially has 9 lit squares. Since each Tetris line clear unlights five squares, this board must be cleared by a number of squares congruent to 1 modulo 5, which can only be achieved by tetromino sequences of length 4 or 9.

The full matchup is:

Switch 1CAPTAIN HOOKTIOO
Switch 2LUMINESCENTLIST
Switch 3ESCAPE VELOCITYSLOIT
Switch 4ARMIN ZOGGELERIZOL
Switch 5ROMEO AND JULIETOOJLIT
Switch 6ALL-SEEINGLLSI
Switch 7LJUBLJANALJLJ
Switch 8LIZ CLAIBORNELIZLIO
Switch 9VIEWTIFUL JOEITILJO
Switch 10INTELLIGENCEITLLI
Switch 11NONCONFORMISTOOOIST
Switch 12ELECTRICAL EQUIPMENTLTILIT
Switch 13STATE LINESTTLI

To finish, we simply re-order the first letters of the answers by the order of the switches they match up to to extract the answer: CLEAR ALL VINES.

## Authors’ Notes

Nathan: When proposing themes for this year's hunt, teams were asked to write a metapuzzle for one of the rounds to go along with their theme. I wrote this puzzle to go along with the "MMO Hunt" proposal (so, in a sense, it was the first puzzle written for this hunt!). Having lived right next to the Green Building for 4 years, it was an easy jump from there to Tetris, and the puzzle fell out pretty cleanly. I don't think it pushes any boundaries, but I'm happy with how it turned out and I hope it was fun to solve.

I remember the Green Building really fondly. If you haven't had the chance to visit yet, try to drop by next time you're on campus! My favorite events were the "Pumpkin Drop" every autumn, where the pumpkins are frozen in liquid nitrogen and spectacularly shatter when they hit the ground, and the "Green Building Challenge", where you repeatedly climb the 24 flights of stairs in the Green Building as many times as you can manage in 2 hours.

Brian: I hacked together a brute-force solver based off hatetris, which caught some boards which had multiple solutions and came up with some interesting instances to replace them.

The solver managed to output several difficult grids, sometimes with absurd-seeming first moves, but we didn’t include them so that people would be able to more easily get confirmation when they tried Tetris. Try them if you want an extra challenge!

Solve with `OOJLIT`:

Solve with `LIZLIO`:

Solve with `LISZTO`: