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Glycereine

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Posts posted by Glycereine


  1. The next step is a proof that these are the only two values that N can assume.

    Congratulations!!!

    Indeed, 7812549630, or 1872549630 are the only two values that N can assume.

    [spoiler='Proof

    ']First, Q,S,U,W and Y must be even numbers (they are the second digit of numbers that must be divisible by a number with a factor of 2.

    Therefore the others must be odd.

    - Y must = 0 as any number divisible by 10.

    - T must = 5 as any number divisible by 5 must end in 0 or 5 (0 is taken by Y)

    - U must = 4, for working down, the only number divisible by 6 that starts with 5 is 54

    - V must = 9 for the only two numbers divisible by 7 that begin with 4 are 42 and 49, but V must be odd (see top)

    - W must = 6 as the only number beginning with 9 that is divisible by 8 is 96

    - X must = 3 because the only number divisible by 9 beginning with 6 is 63

    Simple part is done.

    Now starting back at S, the lowest digit we do not yet know. RS must be divisible by 4 and the only 2 even numbers remaining are 8 and 2. S cannot be 8 because the two odd numbers left, 1 and 7 combined with 8 are not divisible by 4. 18/4 = 4.5 and 78/4 = 19.5

    - S must = 2

    - Q must = 8 as it is the only even number left

    - R can be either 1 or 7 because both 12 and 72 are divisible by 4. Also both 81 and 87 are divisible by 3.

    - P can be anything because no matter what the number starts with PQ will be divisible by 2 if Q is even. Therefore P = 7 or 1 (as well as R = 1 or 7).

    Swapped with each other they make the two possibilities


  2. He has a chance, but it's iffy.

    through my calculations, I get a distance of 61.79km to the base of the monolith. at a rate of 6.2kph, he should get there at 9.966129 hours. this calculates out to 9hours 57minutes and 58 seconds, leaving 2 minutes and 2 seconds. if the lift went up exactly at the moment he reached the base, he'd take 3minutes and 20 seconds to make it into the monolith. I'd say he's got a 60% chance of making it (what if he held his breath for 10 seconds every hour??)

    Skip breathing doesn't reduce the rate of oxygen consumption, in fact it most often increases it. The build up of carbon dioxide furthers the urge to breath and you breath more deeply and quickly than necessary when you cease holding your breath. There are some exceptions if the breath hold isn't too long but figuring he's working fairly hard any breath hold at all would probably not help.

    :). For the record I ended up with 2 minutes 8 seconds but I'm sure it's a rounding issue.

    Chance of survival being then slightly over 60%.


  3. This is counter-balanced by the fact that C has a 1/2 chance of killing D on everyshot. Most of the time, C survives B's shot, so he gets to shoot D. If A kills B, that's even better for C. In this game, killing someone above you is not as important, or urgent, as having someone with low accuracy below you.

    Additionally you said that likely A and E will die in the first round which is not possible. If E dies in the first round, no one can shoot at A because D has already fired his shot (killing E).

    I figured this out for the first 3 rounds using good ole math but then my brain hurt. It kept getting worse with possibilities for each person getting shot at by someone else based on probabilities of each surviving all of the previous rounds.

    After 3 B was looking the best though.

    Prior to doing any math however my guess would have been C.

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