Homesite Puzzler #5: May I Have This St. Vitus Dance?
Posted by Larry Wallberg on 06/15/2010
Today is the feast day of St. Vitus, after whom uncontrollable dancing mania is named. So, to be fair, I decided to throw my readers’ minds into rhythmic spasms. But St. Vitus never constructed any great puzzles that I know of, except the one I played today: trying somehow to tie him into this post.
St. Vitus Dance is, allegedly, one symptom of mercury poisoning. Mercury poisoning was not uncommon among workers in the hat industry, who used mercurous nitrate to help turn fur into felt. Hence, the expression “mad as a hatter.” Aha!
Lewis Carroll, who created the Mad Hatter, loved setting little problems in logical deduction for his child-friends. I don’t see how any of today’s kids could conceivably solve any of those monsters, when they can’t even figure out that it’s impossible to earn a sports trophy just by showing up. So if any of you are children — and if you are, do your parents know you’re reading this? — you’ll probably be thoroughly confused by this puzzle. Hell, even most grown-ups would find it ridiculous. I do, even though I’m dancing as fast as I can.
Carroll’s Symbolic Logic Puzzles consisted of a number of if-then statements (but not always phrased quite so simply) that could be combined in proper sequence to form a logical deduction that was hilarious nonsense. I’ll give you a simple example, and an explanation of the deduction:
1. No one really appreciates mustard unless he loves hot dogs.
2. Nobody who likes Sarah Palin has good taste.
3. If you love hot dogs, you have good taste.
Let’s reduce the phrases to symbols:
Appreciates Mustard = M
Loves Hot Dogs = H
likes Sarah Palin = S
Has Good Taste = T
1. M —> H (If you really appreciate mustard, you love hot dogs.)
2. S —>~T (If you like Sarah Palin, you do not have good taste.)
3. H —> T (If you love hot dogs, you have good taste.)
Remember: The contrapositive of a true proposition is also true. A contrapositive is obtained by reversing the direction of the “implies” arrow, and negating both terms.
So if 2. S —> ~T is true, then
2a. T —> ~S is also true.
Now we can construct a simple string:
M —> H
H —> T
T —> ~S
Assuming that all propositions are true, the deduction is:
If you really appreciate mustard, then you don’t like Sarah Palin.
Or it’s contrapositive: If you like Sarah Palin, then you really don’t appreciate mustard.
Here’s the puzzle. Your job is to assume (obviously, for purposes of this game only) that all the following propositions are true. Then, come up with the final deduction. To be fair to everyone who might want to try this, DO NOT put your answer in a comment. Instead, send it to elwallberg at gmail.com. (As usual, those who arrive at the correct solution will get credit at the bottom of the post.) Of course, you can feel free to leave other types of comments, like “Who the hell is Lewis Carroll?” or “I hate hot dogs unless they’re kosher,” or “Screw you, Wallberg.”
1. Everyone who’s hooked on Chocolate Cheerios loves sweet crunchy things.
2. If you thrive on nonsense, you recite “Jabberwocky” constantly.
3) Unless you long for expensive toys, you’re not a kid at heart.
4) A true Christian loves Jesus.
5) If you’re not hooked on Chocolate Cheerios, you’re a mighty sad person.
6) You must watch a lot of TV commercials, if you long for expensive toys.
7) Love Jesus, and you shall have focus in your life.
8) If you’re not a kid at heart, you don’t love sweet crunchy things.
9) All those who are mighty sad persons have been abandoned by God.
10) Only those who thrive on nonsense watch a lot of TV commercials.
11) If you’ve got focus in your life, you don’t recite “Jabberwocky” constantly.
Happy St. Vitus dancing, all you mad readers out there.