BEIJING TIGERS

We are presented with a list of what are allegedly the best entries to a logic puzzle contest. The flavor text hints at something weird going on in the instructions, and if we read the first and last words of each set of instructions (as hinted by “start” and “end”), we get the cluephrase

FIND ANOTHER CONTEST MIT WON RECENTLY, WATCH BROADCAST AFTER HOUR FOUR, OVERLAP LETTERS FROM FITTING ACRONYM IN SPOKEN ONE MAYBE TWO WORDS WITH TITLES.

The contest being referred to here is ICPC 2021 which took place in Dhaka in November 2022. Shortly after the fourth hour of the broadcast, which can be found on YouTube, commentator ecnerwala / Andrew He starts a recap in which he uses words/phrases that contain the letters I, C, P and C in order while he describes each problem in the contest.

Prob. | Special Word | Words before/after | Video timestamp |
---|---|---|---|

A | MICROSCOPIC | "... crystal structures" | https://youtu.be/15Wyj_-PG9I?t=14074 |

B | INESCAPABLECORRIDORS | "... so if you go into" | https://youtu.be/15Wyj_-PG9I?t=14404 |

C | DISCREPANCY | "not too much ..." | https://youtu.be/15Wyj_-PG9I?t=13746 |

D | PICTUREPERFECT | "might end up with a ..." | https://youtu.be/15Wyj_-PG9I?t=14948 |

E | PICKPOCKETS | "they're not quite ..." | https://youtu.be/15Wyj_-PG9I?t=14742 |

F | CIRCUMSPECT | "maybe should be a little ..." | https://youtu.be/15Wyj_-PG9I?t=16303 |

G | MOSAICPICTURE | "kind of this ..." | https://youtu.be/15Wyj_-PG9I?t=14657 |

H | PICTOGRAPHIC | "... writing system on them" | https://youtu.be/15Wyj_-PG9I?t=13706 |

I | BIOLOGICALPROCESS | "phrased as a ..." | https://youtu.be/15Wyj_-PG9I?t=14331 |

J | INCONSPICUOUS | "a little bit ..." | https://youtu.be/15Wyj_-PG9I?t=14026 |

K | FICKLEPOPULACE | "... full of" | https://youtu.be/15Wyj_-PG9I?t=14817 |

L | LEXICOGRAPHICALLY | "kind of compare them ..." | https://youtu.be/15Wyj_-PG9I?t=13931 |

The words in quotes given at the bottom of the puzzle serve as additional hints to help target the right word/phrase to extract from the broadcast.

Next, we notice that the names of the logic puzzle entries (also conveniently named A through L to match the ICPC problems) are the same length as the special word(s) mentioned by the commentator in the broadcast. Following the instruction from above, we line them up and extract 4 letters from each title as follows:

Prob. | Special Word | Entry Title | Extracted letters |
---|---|---|---|

A | MICROSCOPIC | FORMABRIDGE | ORDE |

B | INESCAPABLECORRIDORS | RECUPERATELOGOEFFORT | RPRO |

C | DISCREPANCY | ABCLINEGAME | BLEM |

D | PICTUREPERFECT | USBKEYSYMPTOMS | SBYM |

E | PICKPOCKETS | CITYSPOWERS | ITSO |

F | CIRCUMSPECT | ELEVENSECTS | LVET |

G | MOSAICPICTURES | THETIMESTONES | IMET |

H | PICTOGRAPHIC | CAKETRADEOFF | AKEF |

I | BIOLOGICALPROCESS | MINDSFIRSTSYSTEMS | IRST |

J | INCONSPICUOUS | LDISCONNECTED | LINE |

K | FICKLEPOPULACE | COFFEEOROPAQUE | OFOU |

L | LEXICOGRAPHICALLY | MOSTPROFOUNDTILES | TPUT |

This gives us the next clue phrase: ORDER PROBLEMS BY MIT SOLVE TIME TAKE FIRST LINE OF OUTPUT.

Now that we have an ordering, we next realize that the unique solutions to each of the logic puzzles given to us can be interpreted as lines for input for each of these problems.

All of the given inputs to the ICPC problems can be solved by hand, requiring at most some math / trigonometry. It is also possible to avoid this manual computation and find solutions to these problems online.

Each output corresponding to the logic puzzle solutions consists of one or more lines, but as directed by the clue phrase we only care about the first line. Each problem’s first line can be interpreted as a single letter using A1Z26 (except for problem C, which gives 2 letters). We can find the times at which the teams solved the problems on the final scoreboard. Ordering the problems by when the team from MIT solved it, we obtain the answer **BEIJING TIGERS**.

Prob. | MIT Time | Extracted letter(s) |
---|---|---|

C | 25 | BE |

L | 30 | I |

H | 43 | J |

A | 50 | I |

J | 69 | N |

I | 106 | G |

F | 122 | T |

G | 166 | I |

B | 184 | G |

E | 196 | E |

K | 248 | R |

D | after contest | S |

- You might have encountered some difficulty finding the special phrase for Problem F - this was because the stream cut out while Andrew was covering this problem! We had to get Andrew to re-mention problem F some 30 minutes later, at timestamp 4:54:30.
- One of the other ideas we had for extraction involved going back to the broadcast. At 3:02:16 of the broadcast, Andrew mentions “The team from Beijing” as having solved problems C, B and L among others. This was originally meant to clue the China Baseball League, but we eventually decided against going this route because the timestamp was too hard to clue.
- Shoutout to Andrew’s cohost SecondThread and the rest of the ICPC Live team for playing along with our scheme to embed puzzle content in the stream!

- The idea for the puzzle was drafted 3 days before the competition itself, when Andrew was already in Dhaka.
- We didn’t know anything about the contest until it started (including how many problems there were and their contents), so when the contest started, we basically had 5 hours to decide what and how to embed puzzle content in the broadcast, and then do it. We had done some ICPC-word brainstorming beforehand, but trying to fit them into a script without sounding suspicious was something that had to be done on the fly. Major props to Andrew for delivering the script so smoothly!

Here are the solutions to all of the logic puzzles.

This table shows the inputs and corresponding outputs for each problem. Note that some inputs can have multiple possible outputs, but the extracted letter is always the same.

Prob. | Input | Output | Extracted Letter(s) | Remarks |
---|---|---|---|---|

A | 26 26 1 3 3 2 2 4 9 1 | ........#................. .......................... .......................... .#........................ .......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... ........#................. .......................... .......................... .#.........#.............. .......................... .......................... ....#.........#........... .......................... .......................... .......#.........#........ .......................... .......................... ..........#.........#..... .......................... .......................... .............#.........#.. .......................... .......................... ................#......... .......................... .......................... ...................#...... .......................... .......................... ......................#... .......................... | I | The first line has 26 characters, with the ninth character being #, giving I. |

B | 5 1 5 2 1 2 3 1 3 4 1 4 1 2 3 5 1 | 7 | G | |

C | 7 1101101 | 2 5 | BE | There are 2 characters in the first line, corresponding to 2 letters. |

D | 4 42 42 13 41 53 53 41 13 23 42 42 23 | 19.000000000000000 | S | This is equal to 19, giving S. |

E | 9 1 725768 | 0.50000000000000000 | E | The part after the decimal point is 5, giving E. |

F | 1 1 3 46888 55748 29099 28125 40948 39827 33310 10245 22438 33310 76082 43949 | 20.00000000000000002605883 | T | This is approximately equal to 20, giving T. (Note that it is not exactly 20, because the arctangent of a rational number cannot be exactly 20 degrees.) |

G | 1 2 2 2 3 4 2 2 2 2 2 2 2 2 2 2 2 2 | 9 1 1 1 2 1 3 2 1 2 2 2 3 3 1 3 2 3 3 | I | |

H | 10 )) )( )( )( )( )( )( )( )( (( | 10 2 3 4 5 6 7 8 9 1 | J | |

I | 31 0 25 | 7 8 9 10 11 12 13 14 15 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 | G | |

J | 45 2 1 S 1 2 3 S 3 4 5 4 4 | 14 | N | |

K | 4 3 2 3 4 0 1 2 0 2 2 0 2 3 | 18 | R | |

L | 4 4 ...X .... ..X. .X.. | 9.0000000000 15 (1,3) (1,4) | I | This is equal to 9, giving I. |