BrainDen.com - Brain Teasers  # harey

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## Everything posted by harey

1. @jasen: a computer simulation for such a problem is IMHO an overkill. Bonanova's approach is correct, he just did not finish it.
2. @bmad: yes, "non-mathematical" equivalence of "the jar is quite large" and "the marbles are quite small" @jasen: In overwhelming majority of cases, I base my decision on probability, very exceptionally on luck. @bonanova: The answer I expected. I would reason something like that: if there is one black marble, p(black)=1/100. Repeating 100 times, I would estimate p(all white) about 95% and would be very surprised if I were told it is less than 90%. Knowing the solution, I recall the problem of n people having birthday the same day. However, your formula is missing something. If you complete it, you will get another surprise. (Please hurry, I do not want to be faced with the problem of two best answers again.)
3. There are 100 (quite small) marbles in a (quite large) jar. Pull out one marble, look at it, put it back. You have done it 100 times. All marbles were white. Would you bet 5:1 that they are all white? Bonus (and most interesting) question: Suppose you have 15-20 seconds to decide.
4. The speed is a real number. As there is an infinity or real numbers, p(two bullets have the same speed)=zero, at least for a "small" n. The same way we do not suppose that 3 (or more) bullets can collide. However, there is something else that gives me headaches. It works when there are n bullets in line AFTER all n bullets were shot. What if the first two bullets collide and then n-2 bullets are shot? More generally, what if there are collisions before all bullets are shot?
5. Yes, the "official" one. But as I know it, it would be unfair to publish it. So I will leave it to someone else. We gave some hints now, did not we?
6. The list of given examples is not exhaustive nor limiting. You can tailor a property to any number and we can argue ad eternum whether this property is interesting or not. Just my personal opinion
7. Well, I know the "official" answer to this problem, but I do not agree with it. Human language is very imprecise, "interesting" is quite subject to interpretation. I.e. my ex does not find 4 interesting at all. 2+2=2*2=2^2? So what?
8. I hope I got it:
9. I calculated very roughly. Interpolating an exponential is quite dangerous. If the temperature was rounded by 0.2 degrees and measured 2-3 minutes before/after the whole hour, you can get quite a different result. Proof is left to the reader.
10. Not necessarily. v3>v2>v1 and diff_1<>diff_2 assumed diff_1=v2-v1 diff_2=v3-v2 if(diff_2>diff_1) then [3 reaches 2] else [2 reaches 1] I just cannot figure out p(diff_2>diff_1).
11. @hhh3: Can you tell how?
12. What about a supplementary rule excluding Fred has 354?
13. I have got 3 solutions, but I do not really understand the point (9)
14. I calculated with 660.60 and the price is 600.60. Just a small typo as I often do...
15. Set aside the sets calculated by Bonanova: 13,519.90-(4*660.60)-(1*1501.50)=9,376 As 600.60*5=1501.50*2=3003=3*1001, remain TVs for 231, 273, 429, 1001 (multiple solutions reserved). 231=3*7*11 273=3*7*13 429=3*11*13 -> all divisible by 3 9+3+7+6=25; so 9,376 is not divisible by 3; -> there are at most 8 TVs priced 1,001 and only 7,374 and 1,368 fits. The same way substract multiples of 231 and consider multiples of 39 (3*13, common divisor of 273 and 429). Alternatively, I think the problem could be solved by Diophantine equations, but I never studied them.