58. FILLED GENERAL 4x4 MAGIC SQUARES (1)
 
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1) Start with this; Note the pattern! Manipulate to this
171214 
281113 
351016 
46 915 
     
 
11271434
13811234
16510334
4961534
3434343434

2) Start with this; Note the pattern!
 
Manipulate to this
1234 
5678 
9101112 
1314 1516 
     
 
11281334
15610334
14711234
4951634
3434343434

3) Start with this; Note the pattern!
 
Manipulate to this
1234 
1314 1516 
9101112 
5678 
     
 
12151634
13143434
121110934
876534
3434343434

4) Start with this; Note the pattern!
 
Manipulate to this
1234 
5678 
9101112 
1314 1516 
     
 
11514434
61297 34
115810 34
162313 34
3434343434

5) Start with this; Note the pattern!
 
Manipulate to this
1234 
5678 
9101112 
1314 1516 
     
 
11514434
7961234
10811534
16231334
3434343434

6) Start with this; Note the pattern!
 
Manipulate to this
1234 
5678 
9101112 
1314 1516 
     
 
11514434
10118534
7691234
16231334
3434343434

7) Start with this; Note the pattern!
 
Manipulate to this
1234 
5678 
9101112 
1314 1516 
     
 
11514434
12679 34
81011534
133216 34
3434343434


These are General 4 by 4 Magic Squares.
In fact, you may fill any 16 consecutive (or equally spaced numbers)!

Perhaps, the last, 7), is the best of all with minimum manipulations?

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


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