Suppose the train has a slanted windshield. With otherwise the same parameters as in the original puzzle, the ball hits the windshield and bounces exactly vertically (as observed by a static observer on the ground). [1] In what angle is the windshield slanted? [2] What will be the upward speed of the ball after having bounced off of the collision?

]]>Instead of writing the maths, I’d refer http://en.wikipedia.org/wiki/Momentum#Elastic_collisions

So, the ball will bounce at 300 km/h backwards. This was so easy…

Interesting tough, what if there’s another tennis ball pirsuing the train at 100 km/h since being tossed by some other guy after the train so precisely so they are touching themselves slightly?

]]>Your answer is correct and elegant. However, there are other correct answers as well. My original answer would have been: “I’m thinking of an odd integer. Does the number (1, 2, or 3) that you are thinking divide it exactly?”

]]>>”The i number isn’t actually relevant, since if it is, the answer could be different for different i, but the puzzle supposes just one solution, so we can stop here now.”

… I don’t completely agree. Because getting 1/2 as a result for i=2 does not guarantee that all i=3..256 share the same result. They happen to, yes, but had they not, then the real answer would have been the weighted average for i=2..256 , no?

]]>First, let’s say the lady (L) is entering right before the man (M), so there are only 2 seats left (i=2). It’s obviousely 1/2. The i number isn’t actually relevant, since if it is, the answer could be different for different i, but the puzzle supposes just one solution, so we can stop here now. 8)

Anyway, add a businessman (B1) between L and M (i=3). Both “outer” variants are 1/3: L found the right place, or L occupied M’s place. But there also two “inner” variants, when L occupies B1’s place. Both symmetrically resolve to 1/3*1/2, since B1 might take a L’s or M’s place. 1/3+1/3*1/2=1/2.

Add another B2 (i=4). Outer: 1/4. Intermediate (one level): 1/4*1/3. Inner (two levels): 1/4*1/3*1/2. Outcome is always symmetrical.

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