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Reverse Partition grouping problem

  1. Mar 12, 2008 #1
    In an Excel group someone connected with the Texas caucus gave this math problem> how to subdivide the following set of precincts into subsets so that there are a maximum number of subsets from this set with each subset of precincts totaling at least 180 votes. Since the caucus is this month it seems like a quick answer is needed.

    ----- Original Message -----
    From: George Lawshe
    To: EXCEL-G@PEACH.EASE.LSOFT.COM
    Sent: Wednesday, March 12, 2008 9:18 PM
    Subject: Voting List


    I am sure all of you have heard about Texas and their "Vote Twice" in the
    Presidential Primary in Texas. Well, it is even more complicated than you
    realize. Each county has several voting precincts and they caucus in March
    to determine who gets additional Delegate votes. This is determined by how
    many people voted in our last governor's race in 2006. If a precinct has
    less than 180 votes then they must be paired with other precincts. This
    means if Pct 2 voted 90 and Pct 3 voted 90, they would be paired.

    Well you can imagine the problems if one has 100 plus precincts to try to
    match them up so each will be at least 180, but as many groups as possible.

    This may be more than Excel can handle, but I thought I would try.

    Please see the list below, I have already filtered out those 180 plus. Is
    there a way to have Excel search and match the precincts, (numbers in left
    column) and show together. Something like:



    10,12=180

    15,16=189

    1,8 =196



    Thanks for your help

    George




    Pct

    Votes


    1

    100


    6

    51


    7

    122


    8

    96


    9

    133


    10

    104


    11

    46


    12

    76


    13

    59


    14

    57


    15

    67


    16

    121


    17

    105


    18

    119


    19

    113


    20

    45


    21

    52


    22

    73


    23

    94


    24

    77


    27

    129


    28

    115


    29

    30


    30

    81


    31

    27


    33

    101


    34

    157


    35

    58


    36

    21


    37

    146


    38

    31


    39

    25


    40

    147


    41

    72


    42

    0
     
  2. jcsd
  3. Mar 12, 2008 #2

    CRGreathouse

    User Avatar
    Science Advisor
    Homework Helper

    With a total of 2850 votes, there can't be any more than 16 groups. I think the maximal number of groups is 15, which is easy enough to make:

    96 57 27
    100 94
    101 81
    104 77
    105 76
    113 72
    115 67
    119 30 31
    121 59
    122 58
    129 52
    133 51
    146 46
    147 45
    157 25

    with the 21 and 73 anywhere you like.
     
  4. Mar 13, 2008 #3
    There are not enough votes for 16 * 180 anyway.
    I solve it easily also and I wonder if this problem is authentic.
     
    Last edited: Mar 13, 2008
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