k-man

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Maybe I wasn't clear, but my solution doesn't involve any curved lines. All straight line segments connecting a blue dot with a red dot and they don't cross.

It's easy to show with n=2 that it's not possible with lines, so I will assume that you meant line segments connecting a red and a blue points.

Nice explanation, plasmid. Marking as solved.

My reasoning was correct, but I just made a silly mistake at the end. BTW, I was just kidding about getting respect, but in my solution I was still assuming that the puzzle was indeed unsolvable 4 years ago.

It's hard to get some respect around here Thanks for a great puzzle and an honorable mention, Bonanova!

Maybe it is. I don't know as I've never heard of it before

Any other thoughts?

It is a well-known fact that the number pi is an irrational number. This means that its decimal representation is infinitely long. 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664... What is the probability that pi's decimal representation contains a sequence of digits ...0123456789....? What is the probability that it contains ...33333333333333333333...?

Bona, It's very unlikely to happen in a finite case, but is almost certain in an infinite case. It won't be exactly 8 - there will be more and there will be new "survivors" that will live maybe even longer that those 8, but they will not survive forever. I think you meant exactly 8 and the 9th will be the new survivor. Yes, I agree with that and that's what will eventually happen, but the new survivor(s) will also not survive forever. My sentiments exactly.

Assuming that 1) The king starts from e8 (the normal starting position for the black King) and 2) Every square is to be visited only once

Can you clarify these points? 1) If there are 2 elevators starting from 50th floor, will 2 people get on the same elevator? 1 on each? Do we have freedom to choose how to distribute people to elevators? 2) If there are 2 or more elevators will they all stop on the 49th floor? Or only one will stop and the others will skip it? If latter, can we choose which elevator will stop on what floor? 3) If the elevator reaches capacity and the floor below doesn't have anyone waiting, will it travel to the next floor that has people waiting? Or will it unload on the next floor below and continue empty? 4) What's the optimization criteria? Are we looking for the minimum number of elevators required to get these people where they want to go in the shortest time possible? Thanks

I knew I was missing something obvious.

Does "combined score" mean the total number of chips Moe and Joe have together after 10 rounds? If so, then the answer is 520, but where is the puzzle? I'm sure that's not the right answer, so I'm not hiding it in the spoiler.

I think Pickett's got it for the square. How about an equilateral triangle?