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Stratego

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  1. I think the problem below is an nCr problem [n!/(r!*(n-r)!)], but I'm not quite sure how to approach it. Any help would be appreciated. There are 20 numbers, 1-20. Someone would randomly pick 5 numbers. I need to create sets of 10 numbers so that at least one set contains the 5 numbers that the other person pick. What's the minimum number of sets I'd need to create?
  2. If a paraplegic gets a mosquito bite on his leg, does the area around the bite swell up? Does swelling require a brain signal to tell the blood to rush to the area, and if it does, does the signal get through in this case?
  3. My understanding of quantum physics is limited to the few weeks I took back in Freshmen year of college, so pardon the simplicity in my thinking. My question is how do we know that in the phenomenon we describe as quantum tunneling, that it's actually the same particle that we observe? The way it was describe to me was to imagine throwing a ball at a wall. Most of the time, the ball will bounce back, but in the quantum level there is a small chance that the ball will pass through the wall and appear on the other side. Could it be that the particle just got absorbed by the "wall" and the "wall" just spit out something that looks like the particle? (Here's where I bring in another aspect of physics where I have little knowledge of) If E=mc^2, could it be that when the particle hits the wall it gets converted into energy, then the energy causes the "wall" to be destabilized, and as it re-stabilizes part of the energy gets converted back to mass, and it just happens to look like the particle that you shot and happens to be on the other side? Basically what I'm asking is equivalent to explaining the phenomenon as throwing a brick at a wall, and having the energy knock out a piece of the wall that looks like that brick.
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