Each line refers to a joke: either of the form "What's the difference between..." or of the form "What do you get when you cross...". The joke is inverted as if it were a mathematical statement, and the punchline is given instead of one of the operands.
What's the difference between roast beef and pea soup? Anyone can roast beef.
Roast beef – Pea soup = Anyone can roast beef
and thus the answer is:
Roast beef – Anyone can roast beef = PEA SOUP
Now, solve the corresponding lightbulb joke — e.g. "How many Harvard Students does it take to change a lightbulb? One — he holds it and the world revolves around him," and use that answer ("one") to index into the joke answer. The first letter of PEA SOUP is P. Continuing in this fashion, we find that the indexed letters spell out "Photons go this fast," so the answer is SPEED OF LIGHT.
Answers (the appropriately indexed letter is capitalized, and the indexes are given in brackets):
Thetitanic (or Titanic) [one]
And the answers to the lightbulb jokes, in the order they appear:
[Harvard students] One — he holds it and the world revolves around him
[MIT professors] Four — one to do it and three to co-author the paper
[Violinists] Three — one to do it and two to stand around and talk about how much faster they could have done it
[Therapists] One, but it's got to want to change
[Grad students] Only one but it takes him nine years
[Schizophrenics] Both of us
[Anticlimaxes] ... I don't know ... about seven?
[Circus performers] Four — One for the money, two for the show, three to get ready, and four to go
[Investment brokers] Three — one to take it out and drop it, and two to try to sell it before it crashes
[Blondes] Five — one to hold it and four to turn the ladder
[Fishermen] Five. And you shoulda seen it — it was this big
[John Kerry] Four. No, two. No, nine.
[Californians] Nine — to do it and eight to pray against the darkness
[Surrealists] Three — one to hold the giraffe and two to fill the bathtub with brightly colored bicycles
[Christians] Three, but they're really one
[Frat boys] Eight — one to hold it and seven to drink 'till the room spins
[Oregonians] Six — one to do it and five to fend off the Californians trying to share the experience
Yes, there are some extra words in the word box — they don't mean anything.
2006 MIT Mystery Hunt