Solved This Before?

If the puzzle you solved before you solved the puzzle after you solved the puzzle you solved before you solved this one was easier than the puzzle you solved after you solved the puzzle you solved before you solved this one, was the puzzle you solved before you solved this one easier than this one? Yes or no?

E4
Let's face it. Some puzzles can't be solved. Puzzles like 'what's the purpose of life?', 'what's the undoing of death?', 'are there other life forms in the universe?' etc. But on a less philosophical scale, you have what is called the 'the mutilated chessboard problem'. It's strictly a tiling puzzle proposed by the philosopher Max Black in his book Critical Thinking, which was later discussed by George Gamow and Martin Gardner in his Scientific American column Mathematical Games. The problem is as follows: Suppose a standard 8x8 chessboard has two diagonally opposite corners removed, leaving 62 squares instead of 64. Is it possible to place 31 dominoes of size 2x1 so as to cover all of these squares? Don't even go there! Here, instead, is a more convoluted puzzle.
If the puzzle you solved before you solved the puzzle after you solved the puzzle you solved before you solved this one was easier than the puzzle you solved after you solved the puzzle you solved before you solved this one, was the puzzle you solved before you solved this one easier than this one? Yes or no?

DEAR MS

(The older problem was: "There is exactly one astronomer on every planet of a certain system. He or she watches the closest planet. The number of the planets is odd and all of the distances are different. Prove that there is one planet not being watched." - MS)
Star-Watchers Dept:
Imagine a simple planetary system with five planets numbered A to E, with no two distances being the same. If the distance AB is less than BC, then astronomers on A and B would watch each other's planet, and C will have to watch another planet, say D, and if CD is less than DE, then C and D would watch each other. Hence, E would go unwatched. If, however, BC is less than AB, and the distances progressively get smaller, B watches C instead of watching A; C watches D, and D watches E. Now either DE is less than EA, or EA is less than DE. If DE is less than EA, E watches D, leaving A unwatched. If EA is less than DE, then E watches A, and no one watches D. This logic can be extended to any number of planets as long as the number is odd.

• Ramesh S Mahalingam,

ramesh@idealmc.com
(The second problem was a logical one concerning six people with varying lifestyles who had a certain breakfast time routine. And guess what? You had to figure it out. - MS)
Breakfast-Of-Champions Dept:
Here is my solution: (1) Cuckoo has coffee at 6:30 while watching the news on TV; (2) Jasmine has cereal at 6:50 while listening to the news on the radio; (3) Shivvy has toast at 7:15 while reading the newspaper; (4) Madhuban has sausages at 7:35 while listening to music; (5) Jog eats bananas at 7:50, silently; (6) Lalit (is he a warden in a school children's hostel?) downs anything available, at 8:30, while shouting at children.

• Dr Vallish B N,

(The third problem was: "When you drop transparent water on your white shirt or top, why does the resulting stain appear darker?")
Light-Stains Dept:
The water fills the part of the fabric that used to be filled by air. It does not really make the fabric darker. Instead, it just makes the fabric more transparent. Therefore, we perceive a wet spot of fabric that has become more transparent as a wet spot of fabric that has become darker.

• Saifuddin S F Khomosi,

saif_sfk@hotmail.com (Not really; check out below... - MS)
Because water forms a film over the surface and, in a way, polishes the surface, reducing the diffused reflection and increasing specularity. Since the spot is reflecting lesser light, it appears darker than the surrounding fabric.

• Alan D'Souza,

iamaland@gmail.com
ENDGAME(S)

1. The boiling point of olive oil is higher that the melting point of tin. So how come it's possible to fry things using a skillet made of tin?
2. Can a human being drown in a pool of (hypothetically, room temperature) liquid oxygen? 

(Mukul can be reached at mukul.mindsport@gmail.com )
 

• Mindsport