1. Standard memberBigDogg
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    10 Mar '22 07:29
    There is an 11-car train. The sum of passengers for any 3 consecutive cars is 99. There are 381 total passengers.

    How many passengers are in car #9?
  2. Joined
    18 Jan '07
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    10 Mar '22 15:151 edit
    @bigdogg said
    There is an 11-car train. The sum of passengers for any 3 consecutive cars is 99. There are 381 total passengers.

    How many passengers are in car #9?
    I'm going to spoiler this whole answer, except for a few hints.

    The first three carriages together must have 99 passengers total. Let's call them A, B and C, so A+B+C=99.
    Now Reveal Hidden Content
    the second, third and fourth carriages must also have 99 passengers. Call the fourth carriage D, we get B+C+D=99=A+B+C, therefore D=A. Continuing this way, the fifth carriage must have B passengers, and so on.
    The whole train is Reveal Hidden Content
    ABCABCABCAB
    , and carriage 9 is Reveal Hidden Content
    C.
    The train as a whole has 4A+4B+3C=381 passengers, but we also know that 3A+3B+3C=3×99=297. Subtracting these, we get A+B=381-297=84.
    Subtracting that again from A+B+C=99, we get C
    , the 9th carriage, Reveal Hidden Content
    =15, as are the 3rd and 6th carriages.
    We cannot determine the numbers for the Reveal Hidden Content
    eight
    other carriages, except that Reveal Hidden Content
    they must add up, for each adjoining pair, to 84
    , and each Reveal Hidden Content
    pair in the same way
    .
  3. Standard memberBigDogg
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    10 Mar '22 15:46
    @shallow-blue said
    I'm going to spoiler this whole answer, except for a few hints.

    The first three carriages together must have 99 passengers total. Let's call them A, B and C, so A+B+C=99.
    Now Hidden content removed The whole train is Hidden content removed, and carriage 9 is Hidden content removed, the 9th carriage, Hidden content remov ...[text shortened]... es, except that [i][b]Hidden content removed, and each Hidden content removed.
    SOLV'D
  4. Joined
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    10 Mar '22 19:24
    @bigdogg said
    SOLV'D
    It was a nice one.
  5. Standard memberBigDogg
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    10 Mar '22 20:04
    @shallow-blue said
    It was a nice one.
    I enjoyed it as well. Takes some thought, but not overly difficult.
  6. Joined
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    10 Mar '22 20:46
    @shallow-blue said
    I'm going to spoiler this whole answer, except for a few hints.

    The first three carriages together must have 99 passengers total. Let's call them A, B and C, so A+B+C=99.
    Now Hidden content removed The whole train is Hidden content removed, and carriage 9 is Hidden content removed, the 9th carriage, Hidden content remov ...[text shortened]... es, except that [i][b]Hidden content removed, and each Hidden content removed.
    I’m impressed and I didn’t even reveal the hidden content!
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