Puzzles quiz!

1. No ticket wins? Imagine a 1000-ticket lottery with one winning ticket. It's possible that Ticket 1 will not win. This is applicable to Ticket 2, and Ticket 3 ... and Ticket 1000 too. But, seen this way, it entails the impossible conclusion that "one ticket wins and no ticket wins". Who described it?

2. Razor's edge. In a town, there is only one barber. Every male shaves himself or goes to the barber. From this it follows that the barber shaves only those who don't shave themselves. So far so good, but we land in a mess when we ask the question "Does the barber shave himself? If the barber does not shave himself, then he must shave himself; but if he does shave himself, then he will not shave himself. Who mentions the barber's paradox in a song?

3. End of head. A trickster god makes a bet with some dwarfs. Should he lose the wager, the price would be his head. The dwarfs win and come to collect his head. He says it's alright, but they have absolutely no right to take any part of his neck. So, where does the head end and the neck begin. The debate is still on, and the god retains his head. What's the term for the logical fallacy involved?

4. Going to Abilene. "Are we going to Abilene?" Yes, that's the decision of a group of people. Nobody actually wanted the trip, but nobody said "No", because everybody mistakenly believed that all the others wanted to go to Abilene; saying "No" would create a conflict. This happens often in all societies, in collective decisions. Who described it?

5. A poll plot. In a voting situation, individual preferences pose a conflict when taken together. Imagine three candidates, A, B and C, and three voters with the following preferences (in decreasing order). Voter 1: ABC. Voter 2: BCA. Voter 3: CAB. Now, if C is chosen as the winner, you can argue B should win instead, since two voters prefer B to C. But by the same argument, A is preferred to B, and C is preferred to A. What's the situation called, and who noted it first?

6. The elevator paradox. Two famous observers in a multi-story building. The one with an office near the bottom thought the first elevator to stop at his floor was most often going down. The one with an office near the top thought it's quite the other way round. This gives the impression that elevator cars are mantled in the middle of the building and sent upwards or downwards to be dismantled, which is not true. Who were the observers?

7. Buttered cat. Cats always land on their feet; buttered toast always lands buttered side down. So, what would happen if you drop a cat from a good height with a piece of toast attached on its back, butter side up? This is the "buttered cat paradox". Who won a Student Academy Award for a film based on a high-school friend's paper on the topic?

8. The same axe. The paradox in "George Washington's axe" revolves around the question whether the axe remains the same axe if it were fitted with a new head and later with a new handle. Sometimes it's called "My Grandfather's Axe", as referred to in a historical novel: "This is my grandfather's axe: my father fitted it with a new stock, and I have fitted it with a new head." Who was the author?

9. Room for you. Hilbert's paradox (after German mathematician David Hilbert) presents a hotel with infinitely many rooms -- all occupied! As the new arrival, you get Room 1. And for that, the staff have to move the current occupant of Room 1 to Room 2, the occupant of Room 2 to Room 3 and so on. What movie expresses it best with the slogan "We're always full, but we always have room for you"?

ANSWERS 1. Henry E. Kyburg (philosopher, computer scientist) 2. Chip Hop (rap) artist MC Plus in "Man Vs Machine" 3. Loki's Wager (Loki is that god, in Norse mythology) 4. US management expert Jerry Harvey in 'The Abilene Paradox' 5. The voting paradox / Marquis de Condorcet (18th century) 6. Physicist Marvin Stern and the very famous George Gamow 7. Kimberly Miner for her 'Perpetual Motion' (2003) 8. Robert Graves in 'The Golden Fleece' (1944) 9. 'Hotel Infinity' by Amanda Boyle (writer/director)

(HT: The New Indian Express)