Tanya Khovanova's Math Blog

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.