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Math Help - Canadian wild strawberries

  1. #1
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    Canadian wild strawberries

    Jack, John and CWS's
    ================
    Canadian Wild Strawberries (CWS) are tiny but tasty.
    A and B each have a jar containing 400 CWS; they decide
    to have a CWS eating race; A wins, swallowing his last
    CWS when B still has 23 left. Took A 13.2 seconds; burp!
    Next, B takes on C, each with a jar containing 261 CWS;
    B wins, C left with 117 CWS (C has a bad toothache).
    Jack: well, John, A took on C next
    John: ya ya I'm sure he did
    Jack: each had a jar containing N CWS's
    John: oh boy
    Jack: wanna try figure out what N is?
    John: not really
    Jack: here's a hint: in the 200 to 500 range, and they
    both swallowed at same speed as in their 1st race
    John: oh ya? (comes back with a printout)
    Jack: A beat C by an integer amount
    John: ya; I figured as much; need another clue
    Jack: the sum of digits of the number of CWS that C had left
    when A finished is equal to this number here
    ...and John knew.
    What is the value of N?
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  2. #2
    Senior Member Mukilab's Avatar
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    I got as far as working out how many A and C ate per second but now I'm at a semi-standstill as I attempt to figure out how to find factors of fractions/recurring decimals.
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  3. #3
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    Quote Originally Posted by Mukilab View Post
    I got as far as working out how many A and C ate per second but now I'm at a semi-standstill as I attempt to figure out how to find factors of fractions/recurring decimals.
    If you're looking for such factors, then you're doing something wrong.
    We're dealing with integers.
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  4. #4
    Senior Member Mukilab's Avatar
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    I received a recurring decimal when finding how many strawberries A and C eat per second.
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    Quote Originally Posted by Mukilab View Post
    I received a recurring decimal when finding how many strawberries A and C eat per second.
    So?
    The "number per second" does not matter.
    What is needed is the A:C ratio; calculated from the given A:B and B:C ratios:
    A / B = 400 / 377 ; B / C = 261 / 144 .... so A / C = 25 / 13 :
    in other words, when A eats 25, C eats 13.

    You're told range is 200 to 500; so you need to find the integer cases; there are 13:
    1) 200 : 104 ; diff = 96 ; sumdigits = 15
    2) 225 : 117 ; diff = 108; sumdigits = 9
    ....
    13) 500 : 260 ; diff = 240; sumdigits = 6
    Last edited by Wilmer; June 11th 2010 at 12:22 AM. Reason: expand!
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  6. #6
    Senior Member Mukilab's Avatar
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    thanks, I didn't think of it that way

    I'll make sure in the future to consider this
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  7. #7
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    SOLUTION:

    Result of A:B and B:C races means A:C = 400:208.
    So, as we're dealing with integers, jars must contain a
    multiple of 25, since 25:13 is lowest.
    There are 13 such possibilities in the 200-500 range:
    Code:
                 A ate   C ate   A-C  SUMDIGITS
                 200     104     96     15
                 225     117    108      9
                 250     130    120      3***
                 275     143    132      6
                 300     156    144      9
                 325     169    156     12
                 350     182    168     15
                 375     195    180      9
                 400     208    192     12
                 425     221    204      6
                 450     234    216      9
                 475     247    228     12
                 500     260    240      6
    ***Only 3 is unique as sum of digits of the differences.
    If Jack had pointed to any of other numbers, John could not have known.
    So N = 250.
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