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4 x 4 square table


jasen
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I was able to find out one part of this question

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However, I have not been able to find the arrangement of the numbers in the four by four grid.

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  On 7/17/2016 at 11:43 PM, Buddyboy3000 said:

I was able to find out one part of this question

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However, I have not been able to find the arrangement of the numbers in the four by four grid.

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Buddyboy3000,
 

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However, as of yet, I, too, have not found the arrangement of the numbers in the four by four grid.

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I believe this is

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Edited by araver
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To attack the problem, first  write the numbers into its prime factors
2 = 2, 3 = 3, 4 = 2.2, 5 = 5
6 = 2.3, 9 = 3.3, 10 = 2.5, 12 = 2.2.3
15 = 3.5, 18 = 2.3.3, 20 = 2.2.5, 25 = 5.5
30 = 2.3.5, 45 = 3.3.5, 50 = 2.5.5 75 = 3.5.5

So all numbers are consist of 3 prime seed 2,3 and 5
Now replace each seed with 3 symbols, A,B and C
So what we get now  is A, B,C,AA,BB,CC,AB,AC,BC,ABB,ACC,BAA,BCC,CAA,CBB, and ABC
There are 12A,12B, and 12C Total symbols, so each line must have 3A,3B and 3C

What we have to do now is
Put  A,B,C,AA,BB,CC,AB,AC,BC,ABB,ACC,BAA,BCC,CAA,CBB, and ABC to a 4x4 square table,
so every horizontal, vertical and diagonal line have 3A,3B, and 3C.

Edited by jasen
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I started with making a 4x4 using the factor distribution numbers DejMar mentioned. After a combination of the above and a lot of guessing. . . 

 

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Edited by Thalia
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  On 7/19/2016 at 4:15 AM, Thalia said:

I started with making a 4x4 using the factor distribution numbers DejMar mentioned. After a combination of the above and a lot of guessing. . . 

 

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If we change Thalia answer with ABC solution, than replacing ABC with permutation [2,3,5], we can get 6 diffrent answers, one of it is as picture bellow

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There are more solutions than the one given by thalia:
 

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Other solutions may (and I believe) exist.

Edited by DejMar
correction of poster
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A note on the distribution of factors and the number of distinct solutions:

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