Friday, April 14, 2006

March 2006: A Lewis Carroll puzzle (solution)

This is the solution to last month's puzzle, A Lewis Carroll puzzle.

The only animals in this house are cats.
Every animal is suitable for a pet, that loves to gaze at the moon.
When I detest an animal, I avoid it.
No animals are carnivorous, unless they prowl at night.
No cat fails to kill mice.
No animals ever take to me, except what are in this house.
Kangaroos are not suitable for pets.
None but carnivora kill mice.
I detest animals that do not take to me.
Animals, that prowl at night, always love to gaze at the moon.

Logical conclusion: I avoid kangaroos.


H: it is in this house
F: it is a cat
G: it loves to gaze at the moon
D: I detest it
A: I avoid it
P: it is suitable for a pet
C: it is a carnivore
N: it prowls at night
T: it takes to me
K: it is a kangaroo
M: it eats mice

The riddle breaks down as follows (note: each sentence can be replaced by its contrapositive).
H --> F
G --> P
D --> A
~N --> ~C
F --> M
~H --> ~T
K --> ~P
M --> C
~T --> D
N --> G

From which we conclude:
~A --> ~D --> T --> H --> F --> M --> C --> N --> G --> P --> ~K

Possible solutions:
If I do not avoid it, then it is not a kangaroo.
If it is a kangaroo, then I avoid it.
I avoid kangaroos.