Saturday, December 5, 2009

Liars, Truthtellers, and Octopuses*

Tanya Khovanova has translated some puzzles from Russian and created some herself. Now I want to try it.

Here's the intro and the easiest of the problems:
... our characters are genetically engineered octopuses. The ones with an even number of arms always tell the truth; the ones with an odd number of arms always lie. ... Not only do octopuses lie or tell the truth according to the parity of the number of their arms, it turns out that the underwater world is so discriminatory that only octopuses with six, seven or eight arms are allowed to serve Neptune. ... our octopuses who worked as guards at Neptune’s palace were conversing:
  • The blue one said, “All together we have 28 arms.”
  • The green one said, “All together we have 27 arms.”
  • The yellow one said, “All together we have 26 arms.”
  • The red one said, “All together we have 25 arms.”

How many arms does each of them have?

If you enjoyed that, go visit Tanya's blog and try the others.

Now it's my turn. Can I do it? My 4 all work at Neptune's also.
  • Aqua says, "Turquoise has 6 arms."
  • Turquoise says, "Blue has 7 arms."
  • Blue says, "Green has 7 arms."
  • Green says, "Aqua has 7 arms."
  • Aqua says, "The truthtellers have the same number of arms as each other."
Not as elegant, but I think it works. (I'm up in the middle of the night, so my brain may not be functioning well enough to do this.) Your turn...

* Wikipedia explains why it's not 'octopi'.

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