59. GENERAL FILLED 4X4 MAGICSQUARES
 
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1) See the pattern.
Pairs of numbers are entered!
  2) See the pattern.
Pairs of numbers are entered!

1 2 15 16 34
13143434
56111234
9107834
3434343434

 
1 2 15 16 34
13143434
12710534
8116934
3434343434

 
3) Note the colour patterns!
Four numbers are entered together.
  3.a) Flip the above around
the 1, 11, 6, 16 diagonal!

1 81213 
1411 7 2 
1510 6 3 
4 5 916 
     

 
114154 
8 1110 5 
12 76 9 
13 2 316 
     

 
4) A slight variation of (3).
Middle columns interchanged!
  4.a) Flip the above around
the 1, 11, 6, 16 diagonal!

112813 
14 711 2 
15 610 3 
4 9 516 
     

 
114154 
12 76 9 
8 1110 5 
13 2 316 
     

 
5) Start with the one on the left. The rows are filled from top to bottom.
Manipulate to the right. Same colours (4 pairs) are interchanged!

1 2 3 4 
5 6 7 8 
9101112 
13141516 
     

 
115 14 434
12 6 7 934
81011 534
13 321634
3434343434

 
6) Order of filling rows different! Row 1, row 4, row 3 and row 2.
2 sets of 2 pairs are interchanged. The result is the same as that of (1)!

1234 
1314 1516 
9101112 
5678 
     

 
121516 34
13143434
56111234
9107834
3434343434

 
7) Left is just as above! Manipulate to get second.

1234 
1314 1516 
9101112 
5678 
     

 
115144 34
6129734
11581034
16231334
3434343434

 
8) Filling vertically, up & down!
Each column starts at a particular square and is filled vertically downwards or upwards

171214 
281113 
351016 
46 915 
     

 
1 12 7 14 34
13811234
16510334
4961534
3434343434

 
9) Start with this. Note the pattern!
First top row is filled; then bottom row; next 3rd row; finally 2nd row.

1234 
1314 1516 
9101112 
5678 
     

 
112714 34
13811234
16510334
4961534
3434343434

For serious readers:
1) You may be able to work out other vatiations
2) You need not memorise all of any one magic-square.
3) There are nice patterns in each; Try to find the pattern.
4) You can fill similar magic squares with any 16 consecutive natural numbers, odd numbers or even numbers etc.


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