Despised Babies Are Eaten by Illogical Crocodiles

Lewis Carroll, who wrote Alice in Wonderland, was a mathematics professor at Oxford University in England. Besides his popular books, he is also known for his puzzles.

Today, our second and last day of the THSP mathematics conference, Job for the Future's Robert Knittle, our presenter, included sample Lewis Carroll puzzles in a booklet he gave us this afternoon. Puzzle #1, supposedly one of the famed professor's simpler ones, aroused my interest.

The puzzle has three implications:

1. All babies are illogical.
2. Nobody is despised who can manage a crocodile.
3. Illogical persons are despised.

Using the three implications listed above, what is the "inescapable" conclusion?

The same booklet offered a solution, but I had the urge to work on it myself. I teach my geometry students about conditional (if-then) statements. Instinctively I thought that the so-called implications are but conditional statements waiting for a proper makeover. I would love for them to know that everything that I had taught them on conditional statements was enough to solve a Lewis Carroll puzzle. :p

Here's how I played it:

I rewrote all three implications into the following if-then statements:

4. If it is a baby, then it is illogical.
5. If you can manage a crocodile, then you are not despised.
6. If you are illogical, then you are despised.

I applied the Law of Syllogism on statements 4 and 6, and it resulted to:

7. If it is a baby, then it is despised.

I compared statements 5 and 7. Since the contrapositive of a conditional statement is logically equivalent to the statement, I decided to write the contrapositive of the former:

8. If you are despised, then you cannot manage a crocodile.

I applied the Law of Syllogism, once again, on statements 7 and 8 to arrive at my "inescapable" conclusion:

9. If it is a baby, then it cannot manage a crocodile.

It is the same as the one presented in the booklet. Yayyy!

In Lewis Carroll's words, that would probably be rephrased as:

No despised baby is spared by illogical crocodiles.

Not really! :D