GRID 3x3, row, column, total must be 14

M

motilulla

Well-known Member
Joined
Feb 13, 2008
Messages
2,422
Office Version
  1. 2010
Hello,

Is it possible to create all possible Grids 3x3 which rows and column total must be 14 using all numbers are in column B, C, D

Apart of creating all possible Grids could be having random option too.

Example below showing 4 examples not necessary show the total of rows and columns it is shown just for example


Book1
ABCDEFGHIJ
1Choice 1Choice 2Choice 3
2059
3068
4077
508605914
609564414
714985114
8158141414
9167
1017665314
1118533814
1219456314
13239141414
14248
1525792314
1626635614
1727527514
18284141414
19293
2032957214
2133834714
2234763514
23356141414
24365
25374
26383
27392
28419
29428
30437
31446
32455
33464
34473
35482
36491
37509
38518
39527
40536
41545
42554
43563
44572
45581
46590
47608
48617
49626
50635
51644
52653
53662
54671
55680
56707
57716
58725
59734
60743
61752
62761
63770
64806
65815
66824
67833
68842
69851
70860
71905
72914
73923
74932
75941
76950
77
78
79
80
81
Sheet2


Thank you all
Excel 2000
Regards,
Moti
 

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Upvote 0
When you find one square, you actually find eight solutions.


Book1
JKLMNOPQR
2A932239E
3257752
4365563
5
6B329572F
7653653
8572329
9
10C563365G
11752257
12239932
13
14D275923H
15356356
16923275
17
Sheet1


E is a mirror image of A. The squares are then rotated clockwise as you go down each column. It should be easy to see that B and H are mirror images, as are C and G, and D and F.
 
Last edited:
Upvote 0
thisoldman said:
When you find one square, you actually find eight solutions.

J
K
L
M
N
O
P
Q
R
A
E
B
F
C
G
D
H

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[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=EBEBEB]#EBEBEB[/URL] , align: right"]5
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[TD="align: center"]7
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[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=EBEBEB]#EBEBEB[/URL] , align: right"]5
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[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=EBEBEB]#EBEBEB[/URL] , align: right"]6
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[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=EBEBEB]#EBEBEB[/URL] , align: right"]5
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[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=EBEBEB]#EBEBEB[/URL] , align: right"]3
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[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=EBEBEB]#EBEBEB[/URL] , align: right"]2
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[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=EBEBEB]#EBEBEB[/URL] , align: right"]9
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[TD="align: center"]9
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[TD="align: center"]10
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[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=EBEBEB]#EBEBEB[/URL] , align: right"]5
[/TD]
[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=EBEBEB]#EBEBEB[/URL] , align: right"]6
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[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=EBEBEB]#EBEBEB[/URL] , align: right"]3
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[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=EBEBEB]#EBEBEB[/URL] , align: right"]3
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[TD="align: center"]11
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[/TD]
[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=EBEBEB]#EBEBEB[/URL] , align: right"]5
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[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=EBEBEB]#EBEBEB[/URL] , align: right"]2
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[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=EBEBEB]#EBEBEB[/URL] , align: right"]2
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[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=EBEBEB]#EBEBEB[/URL] , align: right"]5
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[TD="align: center"]12
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[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=EBEBEB]#EBEBEB[/URL] , align: right"]2
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[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=EBEBEB]#EBEBEB[/URL] , align: right"]9
[/TD]
[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=EBEBEB]#EBEBEB[/URL] , align: right"]3
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[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=EBEBEB]#EBEBEB[/URL] , align: right"]2
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[TD="align: center"]13
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[TD="align: center"]14
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[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=EBEBEB]#EBEBEB[/URL] , align: right"]2
[/TD]
[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=EBEBEB]#EBEBEB[/URL] , align: right"]7
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[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=EBEBEB]#EBEBEB[/URL] , align: right"]5
[/TD]
[TD="align: right"][/TD]
[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=EBEBEB]#EBEBEB[/URL] , align: right"]9
[/TD]
[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=EBEBEB]#EBEBEB[/URL] , align: right"]2
[/TD]
[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=EBEBEB]#EBEBEB[/URL] , align: right"]3
[/TD]

[TD="align: center"]15
[/TD]
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[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=EBEBEB]#EBEBEB[/URL] , align: right"]3
[/TD]
[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=EBEBEB]#EBEBEB[/URL] , align: right"]5
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[/TD]
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[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=EBEBEB]#EBEBEB[/URL] , align: right"]3
[/TD]
[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=EBEBEB]#EBEBEB[/URL] , align: right"]5
[/TD]
[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=EBEBEB]#EBEBEB[/URL] , align: right"]6
[/TD]
[TD="align: right"][/TD]

[TD="align: center"]16
[/TD]
[TD="align: right"][/TD]
[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=EBEBEB]#EBEBEB[/URL] , align: right"]9
[/TD]
[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=EBEBEB]#EBEBEB[/URL] , align: right"]2
[/TD]
[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=EBEBEB]#EBEBEB[/URL] , align: right"]3
[/TD]
[TD="align: right"][/TD]
[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=EBEBEB]#EBEBEB[/URL] , align: right"]2
[/TD]
[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=EBEBEB]#EBEBEB[/URL] , align: right"]7
[/TD]
[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=EBEBEB]#EBEBEB[/URL] , align: right"]5
[/TD]
[TD="align: right"][/TD]

[TD="align: center"]17
[/TD]
[TD="align: right"][/TD]
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[TD="align: right"][/TD]
[TD="align: right"][/TD]
[TD="align: right"][/TD]

</tbody>
Sheet1​



E is a mirror image of A. The squares are then rotated clockwise as you go down each column. It should be easy to see that B and H are mirror images, as are C and G, and D and F.
Click to expand...
thisoldman, but how could be done these by formula or with VBA

Regards
Moti
 
Upvote 0
I'm thinking about it and getting lost. I don't think I can solve it.

These are the seventy-five distinct permutations of three non-negative integers that add to 14 (I don't think I missed any). The first triplet you place in the grid can appear in any of six positions. The choice of the second triplet is limited—it must be compatible with the one already in place. There are five possible positions for this second triplet. ...

These are the fifteen distinct triplet combinations that add to 14. I've listed the number of permutations for each combination.


<tbody>
[TD="class: xl66"][/TD]
[TD="class: xl66"][/TD]
[TD="class: xl66"][/TD]
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[TD="class: xl66"]Permutations[/TD]

[TD="class: xl66, align: right"]0[/TD]
[TD="class: xl66, align: right"]5[/TD]
[TD="class: xl66, align: right"]9[/TD]
[TD="class: xl66"][/TD]
[TD="class: xl66, align: right"]6[/TD]

[TD="class: xl66, align: right"]0[/TD]
[TD="class: xl66, align: right"]6[/TD]
[TD="class: xl66, align: right"]8[/TD]
[TD="class: xl66"][/TD]
[TD="class: xl66, align: right"]6[/TD]

[TD="class: xl66, align: right"]0[/TD]
[TD="class: xl66, align: right"]7[/TD]
[TD="class: xl66, align: right"]7[/TD]
[TD="class: xl66"][/TD]
[TD="class: xl66, align: right"]3[/TD]

[TD="class: xl67, align: right"]1[/TD]
[TD="class: xl67, align: right"]4[/TD]
[TD="class: xl67, align: right"]9[/TD]
[TD="class: xl66"][/TD]
[TD="class: xl66, align: right"]6[/TD]

[TD="class: xl67, align: right"]1[/TD]
[TD="class: xl67, align: right"]5[/TD]
[TD="class: xl67, align: right"]8[/TD]
[TD="class: xl66"][/TD]
[TD="class: xl66, align: right"]6[/TD]

[TD="class: xl67, align: right"]1[/TD]
[TD="class: xl67, align: right"]6[/TD]
[TD="class: xl67, align: right"]7[/TD]
[TD="class: xl66"][/TD]
[TD="class: xl66, align: right"]6[/TD]

[TD="class: xl66, align: right"]2[/TD]
[TD="class: xl66, align: right"]3[/TD]
[TD="class: xl66, align: right"]9[/TD]
[TD="class: xl66"][/TD]
[TD="class: xl66, align: right"]6
[/TD]

[TD="class: xl66, align: right"]2[/TD]
[TD="class: xl66, align: right"]4[/TD]
[TD="class: xl66, align: right"]8[/TD]
[TD="class: xl66"][/TD]
[TD="class: xl66, align: right"]6[/TD]

[TD="class: xl66, align: right"]2[/TD]
[TD="class: xl66, align: right"]5[/TD]
[TD="class: xl66, align: right"]7[/TD]
[TD="class: xl66"][/TD]
[TD="class: xl66, align: right"]6[/TD]

[TD="class: xl66, align: right"]2[/TD]
[TD="class: xl66, align: right"]6[/TD]
[TD="class: xl66, align: right"]6[/TD]
[TD="class: xl66"][/TD]
[TD="class: xl66, align: right"]3[/TD]

[TD="class: xl67, align: right"]3[/TD]
[TD="class: xl67, align: right"]3[/TD]
[TD="class: xl67, align: right"]8[/TD]
[TD="class: xl66"][/TD]
[TD="class: xl66, align: right"]3[/TD]

[TD="class: xl67, align: right"]3[/TD]
[TD="class: xl67, align: right"]4[/TD]
[TD="class: xl67, align: right"]7[/TD]
[TD="class: xl66"][/TD]
[TD="class: xl66, align: right"]6[/TD]

[TD="class: xl67, align: right"]3[/TD]
[TD="class: xl67, align: right"]5[/TD]
[TD="class: xl67, align: right"]6[/TD]
[TD="class: xl66"][/TD]
[TD="class: xl66, align: right"]6
[/TD]

[TD="class: xl66, align: right"]4[/TD]
[TD="class: xl66, align: right"]4[/TD]
[TD="class: xl66, align: right"]6[/TD]
[TD="class: xl66"][/TD]
[TD="class: xl66, align: right"]3[/TD]

[TD="class: xl66, align: right"]4[/TD]
[TD="class: xl66, align: right"]5[/TD]
[TD="class: xl66, align: right"]5[/TD]
[TD="class: xl66"][/TD]
[TD="class: xl66, align: right"]3[/TD]

</tbody>

I was wrong in my previous post, writing that finding one solution gives you eight solutions. Some solutions with repeated digits only give four distinct variations:

[TABLE="class: grid"]
<tbody>[TR]
[TD="align: right"]4[/TD]
[TD="align: right"]4[/TD]
[TD="align: right"]6[/TD]
[TD][/TD]
[TD="align: right"]6[/TD]
[TD="align: right"]4[/TD]
[TD="align: right"]4[/TD]
[/TR]
[TR]
[TD="align: right"]4[/TD]
[TD="align: right"]6[/TD]
[TD="align: right"]4[/TD]
[TD][/TD]
[TD="align: right"]4[/TD]
[TD="align: right"]6[/TD]
[TD="align: right"]4[/TD]
[/TR]
[TR]
[TD="align: right"]6[/TD]
[TD="align: right"]4[/TD]
[TD="align: right"]4[/TD]
[TD][/TD]
[TD="align: right"]4[/TD]
[TD="align: right"]4[/TD]
[TD="align: right"]6[/TD]
[/TR]
[TR]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[/TR]
[TR]
[TD="align: right"]4[/TD]
[TD="align: right"]6[/TD]
[TD="align: right"]4[/TD]
[TD][/TD]
[TD="align: right"]4[/TD]
[TD="align: right"]6[/TD]
[TD="align: right"]4[/TD]
[/TR]
[TR]
[TD="align: right"]6[/TD]
[TD="align: right"]4[/TD]
[TD="align: right"]4[/TD]
[TD][/TD]
[TD="align: right"]4[/TD]
[TD="align: right"]4[/TD]
[TD="align: right"]6[/TD]
[/TR]
[TR]
[TD="align: right"]4[/TD]
[TD="align: right"]4[/TD]
[TD="align: right"]6[/TD]
[TD][/TD]
[TD="align: right"]6[/TD]
[TD="align: right"]4[/TD]
[TD="align: right"]4[/TD]
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</tbody>[/TABLE]
 
Upvote 0
thisoldman said:
I'm thinking about it and getting lost. I don't think I can solve it.
Click to expand...
Hello thisoldman, thank you for your efforts

I think it's difficult to make all manually, may some one can understand the idea, and give VBA solutions

Regards
Moti
 
Upvote 0
Hello everyone,

Search into MrExcel there is no VBA solution for 3x3 square which rows and column sums = 14
Goggled there is no such VBA in the entire goggle.
You tube also doesn't found any video regarding my request.

Please need help

Regards,
Moti
 
Upvote 0
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