Fall 2008 Problem 7: If A, then B....
Our puzzle this week is a syllogism from Lewis Carroll (the author of Alice In Wonderland). A syllogism (for our purposes) is a collection of statements that, when read correctly, chain together to create one argument. The most famous syllogism I know is the following:
- All men are mortal.
- Socrates is a man.
- Thus, Socrates is mortal.
Given the below collection of statements from Lewis Carroll, what conclusion (involving all the statements) can we reach?
- No shark ever doubts that he is well fitted out.
- A fish, that cannot dance a minuet, is contemptible.
- No fish is quite certain that it is well fitted out, unless it has three rows of teeth.
- All fishes, except sharks, are kind to children.
- No heavy fish can dance a minuet.
- A fish with three rows of teeth is not to be despised.
Solution
No one got the complete solution. You can convert the above statements into the following:
- 5th statement: If heavy fish, then cannot dance minuet.
- 2nd statement: If cannot dance minuet, then contemptible/despised.
- 6th statement: If contemptible/despised, then not three rows of teeth.
- 3rd statement: If not three rows of teeth, then doubts it is well fitted out.
- 1st statement: If doubts it is well fitted out, then not a shark.
- 4th statement: If not a shark, then kind to children.
Thus, following the implications: all heavy fish are kind to children.
Chris Patterson came close to the correct answer, earning 2 points. From non-students, Chris Evert gave the correct answer.