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  1. #101  
    Ok, bit of overnight activity, but still no (confirmed correct) answer to the clock one.
    I might break out a really hard puzzle today though, just have to make sure I have the answer handy.
    Animo et Fide
  2. mako's Avatar
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    #102  
    It seems to me as though the first few guesses were the closest. In 12 hours, you'd expect 144 possible times (every ~5.0833 minutes, I suppose):

    12.00 = 12.00
    ~12.06 = ~1.01
    ~12.11 = ~2.01
    ~12.16 = ~3.01
    .
    .
    .
    ~12.56 = ~11.04
    ~1.01 = ~12.06
    ~1.06 = ~1.06
    .
    .
    .
    ~11.39 = ~7.58
    ~11.44 = ~8.59
    ~11.49 = ~9.59
    ~11.54 = ~10.59

    and then 12.00 = 12.00 again. But that doesn't really count, so you actually only have 143 times per 12 hours. So, in a whole day, instead of 288, it's 286.

    So I say 286. But I'm staring at this through the insomnia haze of 5.30am, so I don't know if I'm missing some big chunk of brain teaser-y-ness. Maybe Zurich didn't even HAVE trams in 1910!
  3. #103  
    Don't be too intimidated by the presence of Einstein in the puzzle, he was a brilliant physicist but as he said himself his maths skills weren't up to much. I'm sure he was still miles better than me but he was no mathematician.
    Animo et Fide
  4. #104  
    Okay, a hard one from me.
    Consider the two sentences: "The number of a's in this sentence is one" and "The number of e's in this sentence is seven". The first of those sentences is true and the second is false. We consider all the possible sentences of the form of those two sentences with any one of the 26 letters of the alphabet in place of a and e and any word for a number between 1 and 20, inclusive, at the end of the sentence. So we are looking at 26 * 20 = 520 sentences in all.
    How many of these sentences are true?
    Animo et Fide
  5.    #105  
    Quote Originally Posted by PeterBrown
    Okay, a hard one from me.
    Consider the two sentences: "The number of a's in this sentence is one" and "The number of e's in this sentence is seven". The first of those sentences is true and the second is false. We consider all the possible sentences of the form of those two sentences with any one of the 26 letters of the alphabet in place of a and e and any word for a number between 1 and 20, inclusive, at the end of the sentence. So we are looking at 26 * 20 = 520 sentences in all.
    How many of these sentences are true?
    Is there another way than trying (looking at the various sentences and counting letters)?
  6. #106  
    You can turn it into a formula.
    Animo et Fide
  7.    #107  
    Quote Originally Posted by PeterBrown
    You can turn it into a formula.
    ONE formula or several? If it is one, I am impressed, no idea what it could be. I am not a mathematician, but if you ask a mathematician what 1 plus 1 is, he will think for a while and then say happily: Cool, there is a solution! In this case, I see a solution (counting letters and checking which sentences are true), but not an elegant one... If it takes more than, say, five formulas, then it sounds like too much work for me, I give up, sorry...
  8. #108  
    clulup,
    if you manipulate your formula it turns out to be the same as Mako's.

    multiply the entire equation by 2/2 and you will get:

    (1440*143)/720 = 2*143

    This is consistant with what Mako said. The only problem with the logic is: why did he subtract one for the first and second half of the day. According to his logic, you should only take one off for the entire day. So, his answer should actually be 287. Am I missing something?
  9. #109  
    PeterBrown,
    Is this a trick question? there are only 13 distinct letters in the sentence, not including the one in question. So, there are definitely only 26 possible sentence of the given form that can be true. Everything else is false. I must be dumb 'cause I'm not following.
  10. procure's Avatar
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    #110  
    Quote Originally Posted by Chick-Dance
    A teacher meets with 23 new students when they arrive. She tells them, "You may meet today and plan a strategy. But after today, you will have no communication with one another.

    “One classroom contains two light switches labeled A and B, each of which can be in either the 'on' or the 'off' position. BOTH SWITCHES ARE IN THEIR OFF POSITIONS NOW. The switches are not connected to anything.

    "After today, from time to time whenever I feel like it, I will select one student at random and escort her/him to that classroom. This student will select one of the two switches and reverse its position. He/she must move one, but only one of the switches. He/she can't move both but he/she can't move none either.

    "No one else will enter the classroom until I lead the next student there, and he'll be instructed to do the same thing. I'm going to choose students at random. I may choose the same student three times in a row, or I may jump around and come back."

    "But, given enough time, everyone will eventually visit that classroom as many times as everyone else. At any time any one of you may declare to me, 'We have all visited the classroom.'

    "If it is true, then you will all get an A+ in this class. If it is false, and somebody has not yet visited the switch room, you will spend a full day with ACDriver."
    Answer please???
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