Tanya Khovanova's Math Blog

Joseph DeVincentis heard my prayers and created an index for MIT mystery hunt puzzles. He created it not because I requested it, but rather because he was on the writing team this year and they needed it. Anyway, finally there is an index.

I have to warn you, though, that this index was created for people who have already solved the puzzles, so the index contains hints for many of the problems and, on rare occasions, solutions.

Now I will do the math index for this year, and I promise that I will avoid big hints.

• Fun with Numbers — I got a very warm feeling from this puzzle. Some questions were right from my Number Gossip page and I knew some answers by heart.
• Planar Complex — A puzzle with complex numbers.
• Seeking Syren Scotchy — An advanced non-rectangular Nurikabe variation with colors and knight’s moves.
• Side by Side by Side — A massive logic puzzle.
• Counter Culture — So as not to reveal much info, I will just say that some math is involved in solving this puzzle.
• Expeditions — A logic puzzle that requires extra knowledge.
• Lighten Up — A Light-Up variation.
• Directions — I shouldn’t say.
• Message From Above — A math puzzle at the second stage.
• The Prodigious Riddle of Juno — A logic puzzle with a lot of if-then clauses.
• Bulls and Cows — Not surprisingly, a variation on Bulls and Cows
• Building a Mystery — Create a polyhedron.
• Trance State — Logic gates.
• Sequencer — Mirrors.
• 20,000 Leagues Under the Sea — A Battleship puzzle at the second stage.

I love the MIT Mystery Hunt. I like the adrenalin rush when solving problems under pressure. Plus, I like the togetherness of doing problems with other people. During the hunt I usually do not have time to look at all the puzzles: some of them are solved by my teammates while I’m sleeping and others are solved before I get to see them.

I’ve never tried to go back and check out the puzzles I missed nor the puzzles from the previous hunts, probably because without the goal of winning and without my team, I might find them boring. Often the solving process involves tedious Internet browsing to identify the images of different people or objects. I would only be motivated if the puzzle were related to something I am very interested in, such as Ballroom dancing. But I’m not thrilled at the thought of browsing through all the problems in order to find one that is relevant to the Tango.

In short, I need an index to the puzzles. For example, it would be nice to direct the lovers of square dancing to the Do Sa Do puzzle, or fans of Star Trek to the Alien Species puzzle. I hope that nobody blames me for hinting that those aliens are from Star Trek. I’m convinced that Trekkies who only want to solve Star Trek-related puzzles would immediately recognize them anyway. I do believe that I am not revealing too much by saying that the Facebook puzzle will appeal to the aficionados of the television show “24”.

It would be extremely useful to humanity to at least mark the MIT Mystery Hunt puzzles that are self-consistent, and do not require activities. For example, some of the puzzles involve interaction with headquarters, so you can’t solve them after the hunt. Some of the puzzles might expire, as for example the puzzle with pictures of different announcements in the infinite corridor.

Unfortunately, such an index doesn’t exist, and I do not have the time or expertise to create one myself. But I can fill this void at least partially by presenting a guide to math puzzles from the previous four hunts. I can’t promise that my guide is complete, as navigating the MIT Mystery Hunt website is very tiresome.

Before going into the math puzzles, I would like to list Sergei’s favorite type of puzzle: Duck Konundrums. The first Duck Konundrum puzzle appeared in 2000. It was created by Dan Katz, which is why his initials are in the title. One really needs to follow the instructions for this puzzle. This is very unusual as traditionally hunt puzzles do not have instructions at all. Do not be relieved: the instructions are really very complicated. The next Duck Konundrum puzzle appeared in 2002 and was considered to be even more amusing. People loved it, and this type of puzzle became a tradition in subsequent hunts. Here is my list of Duck Konundrums:

• 2000 — 5.6: The Duck Konundrum.
• 2002 — D2: The Mighty Duck Konundrum.
• 2004 — D3: The Fellowship Of The Duck.
• 2006 — The Cock Conundrum — A combination of the Duck Konundrum and a cute boys’ puzzle.
• 2007 — D4: Ducks Playing Poker.
• 2008 — Mystery Rallye — A Duck Konundrum style puzzle without ducks.
• 2009 — The Amazing Juggling Troupe Of Duckkon Undrum V.

Many Mystery Hunt puzzles appeal to mathematicians. I have to warn you though. Puzzles often are divided into two stages. In the first stage, you need to solve a puzzle, like solving sudoku, a crossword or finding all the wedding dates of the people in the pictures. The second stage requires you to produce a word or a phrase that is the answer to the puzzle. The second stage might be as simple as listing the people in chronological order of their wedding dates and then taking the first letters of their last names. This second stage could also be quite difficult. Depending on your tastes one stage of the puzzle might be much more rewarding than the other. If you love solving sudokus, you might find it more fun to just stop with that solution, instead of continuing on to the second stage.

2006

• Got Your Number — Some recognizable numbers at the second stage (my favorite for the year).
• 783658 — Sudoku at the second stage.
• Hey, Look, A Grid! — A bunch of numbers in a grid.
• Feel Your Way — A very frustrating minesweeper.
• Gross Solitaire — A tedious logic puzzle.
• All for One and One for All — The “26L. in the A.” type of puzzle with first-order logic notation.
• Fun with Formulae — Decipher recognizable formulae.
• Numeracy — A list of very big numbers.

2007

• Clash of the Titans — A mixture of skyscraper type puzzles with logic.
• A Midterm Progress Report to the Enron Board of Directors, July 2000 — Many logic puzzles involving numbers.
• Captain Red Herring’s Buried Pirate Booty — A variation of battleship puzzles.
• The Joy of Accountancy — A kakuro variation.
• Splits and Mergers — A combination of mazes.
• Nur einzelne Zahlen erlaubt! — A sudoku-related puzzle.
• Transmogrifiers — Figure out unknown functions.
• Puzzle Editing — A real treat! You need to solve several Japanese puzzles: Fillomino, Nurikabe, Masyu, Light Up, Heyawake, Hitori and Edel.
• Man, I Hate These %#!&@ Sudokus! — You need the extra pdf file to solve these interrelated sudoku puzzles.
• I Only Get a Measly $200? — A logic puzzle related to the Monopoly games requires an extra pdf file.

2008

• Knots and Crosswords — As it says: crosswords with some knots.
• Cursed — A kakuro variation.
• The Cult of Helios — First you have to figure out what this puzzle is about.
• Bad Beat Jackpot — Some poker math.
• Twisty Little Passages — Map the maze.
• Chimera — An interesting mixture.
• Trouble in Triplicate — Related to the game of Set.
• War Game — A logic puzzle.
• All Geared Up — You need to be good with arithmetic to count all rotations.
• Functions — This is my favorite of the year, especially good for sequence fans.

2009

• Cloaked Battleships — A variation on battleship puzzles.
• Growth Involves Reconstructing Legos — A variation on skyscraper puzzles.
• Mos Eisley Spaceport — A graph-fitting puzzle.
• Malthusian Catastrophes — Requires a lot of calculations.
• Plan 4 From Outer Space — You need to solve a lot of equations.
• The Sexaholics of Truthteller Planet — A logic puzzle, my favorite for the year.
• Cross Something-Or-Others — Eight beautiful variations of kakuro. To get to the answer you need to use three more pages: first, second and third. This one was my second favorite of the year.
• Our Crew Is Replaceable. Your Package Isn’t. — Six river crossing puzzles.
• His Alien Barbarian Girl and Her Robot Dog — The puzzle is a colorful version of battleship puzzles. To get to the answer you need to combine this puzzle with its matching doctor puzzle.
• His Troubled Teen — A nice logic puzzle. To get to the answer you need to complement this with the matching doctor puzzle.
• His Investigative Journalist — Jigsaw sudokus, but you have to work to get to them. To get the answer you need to solve the matching doctor puzzle.

It would also be nice to have some ratings for puzzles. I am not sure how to persuade the webmasters of the MIT Mystery Hunt page to do the index and the rating. Feel free to send them an encouraging email.

I love “Knights and Knaves” logic puzzles. These are puzzles where knights always tell the truth and knaves always lie. A beautiful variation of such a puzzle with Gnyttes and Mnaivvs was given at the 2009 MIT mystery hunt. In this puzzle people’s ability to tell the truth changes during the night depending on the sex partner. You will enjoy figuring out who is a Gnytte or a Mnaivv for each day, who is infected and who slept with whom on each night. Just remember that the ultimate answer to the puzzle is a word or a phrase. So there is one more step after you solve the entire logic part. You do not really need to do this last step, but you might as well. Here we go:

The Sexaholics of Truthteller Planet

Each inhabitant of Veritas 7, better known as the Truthteller Planet, manifests one of two mutations: Gnytte or Mnaivv. Gnyttes always tell the truth, and Mnaivvs always lie. Once born a Gnytte or Mnaivv, the inhabitant can never change…until now.

Veritas 7 is in the midst of an outbreak of a nasty virus dubbed Nallyums Complex II. If an infected inhabitant has sex with another inhabitant of that planet, each one can be converted from Gnytte to Mnaivv, or Mnaivv to Gnytte, as shown below:

• If the sex is heteroverific (1 Gnytte and 1 Mnaivv), both become Mnaivvs.
• If the sex is homoverific (2 Gnyttes or 2 Mnaivvs), both become Gnyttes.

This occurs if either party or both parties have the disease. The disease itself is not transmitted via sex, which is some relief.

Several members of a Veritas 7 village have just contracted Nallyums Complex II. Below are statements from the 15 village residents, taken over the 5-day period since the outbreak. Interviews were taken each morning, and sex occured only at night. Each night, residents paired off to form seven separate copulating couples, with one individual left out. No individual was left out for more than one night.

Can you identify the infected individuals and track their pattern of sexual activity?

A note on wording: If someone refers to sex with someone who was a Gnytte or Mnaivv, they are referring to the individual’s truth-telling status just before sex. If a clue says that two individuals had sex, it means they had sex with each other. “Mutation” refers to the individual’s current status as Gnytte or Mnaivv.

Interviews Day 1

• Artoo: Etrusco is not infected.
• Bendox: Cravulon and Flav are not the same mutation today.
• Cravulon: Either Artoo or Flav is a Gnytte today.
• Dent: Jax-7 and I are both Mnaivvs today.
• Etrusco: Greasemaster is a Mnaivv today.
• Flav: There are at least five Mnaivvs today.
• Greasemaster: Murgatroid is a Gnytte today.
• Holyoid: Etrusco is either an infected Mnaivv or an uninfected Gnytte today.
• Irono: Etrusco is a Mnaivv today.
• Jax-7: Among Artoo, Greasemaster, and Nebulose, exactly one is a Gnytte today.
• Killbot: Bendox is a Gnytte today.
• Lexx: Holyoid and Irono are not the same mutation today.
• Murgatroid: There are at least eight Gnyttes today.
• Nebulose: Murgatroid is a Mnaivv today.
• Oliver: Lexx is a Gnytte today.

Surveillance Night 1

Security cameras revealed that Jax-7 did not have sex with anyone last night, and that Nebulose and Murgatroid had sex.

Interviews Day 2

• Artoo: Last night, I did not have sex with an infected individual.
• Bendox: Last night, Oliver had sex with someone who was a Mnaivv.
• Cravulon: There are at least six Gnyttes today.
• Dent: If there are only five Gnyttes today, then Cravulon and Oliver had sex last night.
• Etrusco: Last night, Bendox had sex with someone who was a Mnaivv.
• Flav: Neither Killbot nor her partner last night is infected.
• Greasemaster: Last night, either Cravulon and Bendox had sex, or Oliver and Etrusco had sex, but not both.
• Holyoid: Last night, I had sex with someone who was a Gnytte.
• Irono: Last night, I did not have sex with Flav.
• Jax-7: Last night, Artoo had sex with Dent.
• Killbot: Last night, I had sex with someone who was a Mnaivv.
• Lexx: Cravulon is infected.
• Murgatroid: Nebulose is not infected.
• Nebulose: Last night, either Cravulon or Flav had sex with Etrusco.
• Oliver: Last night, Irono had sex with someone who was a Mnaivv.

Surveillance Night 2

Security cameras revealed that Holyoid did not have sex with anyone last night, and that Irono and Oliver had sex.

Interviews Day 3

• Artoo: Last night, I had sex with the individual who had sex with Murgatroid on Night 1.
• Bendox: Last night, I had sex with an uninfected individual.
• Cravulon: Last night, Jax-7 had sex with the individual who had sex with Lexx on Night 1.
• Dent: Last night, I had sex with someone who was a Mnaivv.
• Flav: Last night, I had sex with an uninfected individual.
• Holyoid: Neither Oliver nor Irono is infected.
• Irono: Last night, the individual who had sex with Oliver on Night 1 had sex with someone who was a Mnaivv.
• Jax-7: There are more than seven Gnyttes today.
• Killbot: Bendox and Murgatroid are the same mutation today.
• Lexx: Last night, the individual who had sex with Flav on Night 1 had sex with an infected individual.
• Nebulose: The individual who had sex with Etrusco on Night 1 is a Mnaivv today.
• Oliver: Last night, Lexx had sex with the individual who had sex with Bendox on Night 1.

Surveillance Night 3

Security cameras revealed that Dent and Jax-7 had sex.

Interviews Day 4

• Artoo: There are at most seven Gnyttes today.
• Cravulon: Last night, I had sex with someone who has never been a Gnytte.
• Dent: The two sex partners of an individual who was a Mnaivv on the first three days had sex last night.
• Etrusco: Last night, Oliver did not have sex.
• Flav: Last night, I had sex with an infected individual.
• Greasemaster: There are exactly eight infected individuals.
• Killbot: None of the individuals who have been left out of the sexual activity is infected.
• Murgatroid: Last night, I had sex with someone who was a Gnytte on Day 1.
• Nebulose: Last night, I had sex with someone who has had sex with Artoo.
• Oliver: Last night, an individual who had sex with Holyoid during one of the first two nights had sex with an individual who had sex with Jax-7 during one of the first two nights.

Surveillance Night 4

Security cameras have been vandalized.

Interviews Day 5

• Artoo: Last night, I had sex with a Mnaivv, but not the individual who, on Night 3, had sex with the individual who, on Night 2, had sex with the individual who, on Night 1, had sex with Dent.
• Bendox: Last night, Dent had sex with the individual who, on Night 1, had sex with the individual who, on Night 3, had sex with the individual who, on Night 2, had sex with Artoo.
• Cravulon: Last night, Holyoid had sex with the individual who, on Night 3, had sex with the individual who, on Night 2, had sex with the individual who, on Night 1, had sex with Murgatroid.
• Dent: Jax-7 is a Gnytte today.
• Flav: Last night, Cravulon did not have sex with the individual who, on Night 1, had sex with the individual who, on Night 2, had sex with the individual who, on Night 3, had sex with Cravulon.
• Jax-7: Last night, Greasemaster did not have sex.
• Nebulose: Last night, Killbot either had sex with an uninfected individual or did not have sex.

My favorite puzzle at 2008 MIT Mystery Hunt was the puzzle named Functions. Here is this puzzle:

36 -> 18      A,B
2 -> 1        A,C,G,H,K,L,O
512 -> 256    A,C,H
4 -> 2        A,G,H,Q
320 -> 160    A,R
411 -> 4      B,E,Q
13 -> 3       B,G,K
88 -> 11      C,D
45 -> 9       C,D,F,J,L
48 -> 6       C,G,M,P,Q
4 -> 1        C,K,L,N,O
36 -> 9       D,E,F
66 -> 8       D,E,G,I
10 -> 3       D,G,L
1 -> 3        D,L
150 -> 15     D,M
3 -> 2        E,H,J,K
25 -> 3       E,K,L,N,Q
9477 -> 14    E,M
129 -> 4      E,N,P
55 -> 10      F,J
411 -> 6      F,K,L,M,N
2002 -> 4     F,O,Q
79 -> 8       G,I,L,P
25 -> 20      H,M
176 -> 80     H,R
3665 -> 8     I,N,Q
7 -> 3        K,Q
11 -> 5       L,M
501 -> 2      L,O,P,Q
8190 -> 5     M,O
180 -> 3      O,P
50 -> 10      R

? -> (?)      F,R
(?) -> ?      J,L
(?) -> ?      A,F
(?) -> ?      N,O,Q
? -> (?)      A,D,J
(?) -> ?      D,H
(?) -> ?      G,K,Q
? -> (?)      B,D,M
(?) -> ?      E,H
? -> (?)      D,F,G,L
? -> (?)      C,G,P