Numerical Zero
Balance: Numerical Zero Balance
means some numbers combination in 3x3 or 4x4 or 5x5 square shape which always
would follow some specific properties.
Firstly we work with
3x3 numerical zero-balance table like below for understand:
Table of Zero balance:
Table of Zero balance:
a11
|
a12
|
a13
|
a21
|
a22
|
a23
|
a31
|
a32
|
a33
|
Here the below
equations are satisfied :
1. a11 +a12+
a13= 0 4. a11 +a21+
a31= 0 7. a11 +a22+
a33= 0
2. a21 +a22+
a23= 0 5. a12 +a22+
a32= 0 8. a13 +a22+
a31= 0
3. a31 +a32+
a33= 0 6. a13 +a23+
a33= 0
9. a11 +
a12+ a13 + a21 + a22 + a23
+ a31 + a32+ a33 =
0
10. a11 +
a33= 0 11. a13 +
a31= 0
12. a21 +
a23= 0 13. a12 +
a32= 0
14. a22+ a33= 0
One can get easily
find out the values are
1
|
-4
|
3
|
2
|
0
|
-2
|
-3
|
4
|
-1
|
& Finally
1+n
|
-4-n
|
3+n
|
2+n
|
0
|
-2-n
|
-3-n
|
4+n
|
-1-n
|
n= 1,2,3,4,………….∞
So, There are
infinite numbers of 3x3 shape numerical zero-balance data.
But the wonder of
specialities belongs to 4x4 shape numerical zero-balance data.
Table of Zero balance:
a11
|
a12
|
a13
|
a14
|
a21
|
a22
|
a23
|
a24
|
a31
|
a32
|
a33
|
a34
|
a41
|
a42
|
a43
|
a44
|
Find out the value of
a11,a12,a13,a14,a21,a22,a23,a24,a31,a32,a33,a34,a41,a42,a43 &
a44.
Where a11≠a12≠a13≠a14≠a21≠a22≠a23≠a24≠a31≠a32≠a33≠a34≠a41≠a42≠a43≠a44≠0
and
a11+a12+a21+a22 =
0, a12+a13+a22+a23 =
0, a13+a14+a23+a24 =
0,
a21+a22+a31+a32 =
0,
a22+a23+a32+a33 = 0, a23+a24+a33+a34 =
0,
a31+a32+a41+a42 =
0,
a32+a33+a42+a43 =
0, a33+a34+a43+a44 =
0,
a11+a21+a41+a24 =
0,
a21+a31+a24+a34 =
0, a31+a41+a34 +a44=
0,
a11+a12+a41+a42 =
0, a12+a13+a42+a43 =
0, a13+a14+a43+a44 =
0,
a11+a21+a14+a24 =
0, a21+a31+a24+a34 =
0, a31+a41+a34+a44 =
0,
a11+a22+a33+a44 =
0, a14+a23+a32+a41 =
0, a11+a14+a41+a44 =
0,
a11+a13+a31+a33 =
0, a12+a14+a32+a34 =
0, a21+a23+a41+a43 =
0,
a22+a24+a42+a44 =
0, a12+a21+a34+a43 =
0, a13+a24+a31+a42 =
0,
a11+a24+a33+a42 =
0, a13+a22+a31+a44 =
0, a14+a21+a32+a43 =
0,
a12+a23+a34+a41 =
0,
a11+a33 = 0,
a22+a44 =
0, a14+a32 =
0, a41+a23 =
0,
a12+a34 = 0, a13+a31 =
0, a21+a43 =
0, a42+a24 =
0
Component’s sum of
every row and column is zero & above all
a11+a12+a13+a14+a21+a22+a23+a24+a31+a32+a33+a34+a41+a42+a43+a44 =
0
Total 48 zero
equations satisfied the table’s numerical combination.
Note: The beginning number may be ±n (where n=1,2,3,............∞), as one can choose.
Note: The beginning number may be ±n (where n=1,2,3,............∞), as one can choose.
(There are billion
billion actually infinite numerical combination fulfills those conditions. Let
find out a single one. If one gets any combination then he may find out every
combination which fulfills all of those conditions.)
Finaly today 26-5-2015, time 10.00AM, BST, I'm going to reveal the correct answer of above post.
The answer belows here:
The answer belows here:
1 | -3 | 7 | -5 |
-2 | 4 | -8 | 6 |
-7 | 5 | -1 | 3 |
8 | -6 | 2 | -4 |
Thanks to all who have tried hard to solve ever.