# Reverse Partition grouping problem

## Main Question or Discussion Point

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

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

## Answers and Replies

Related Linear and Abstract Algebra News on Phys.org
CRGreathouse
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.

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.
There are not enough votes for 16 * 180 anyway.
I solve it easily also and I wonder if this problem is authentic.

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