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arithmetic – What number of conceivable choice of answers a 4×4 field have such that digits will have to now not be repeated 4 horizontally 4 vertically and a couple of lengthy diagonally


assume i’m given a collection of four knowledge’s
let A = {1,2,3,4}
now what number of answers i will make such that the information redundancy in the entire 4 vertical , 4 horizontal and a couple of diagonal route is 0

instance
assume i’ve B = {1,2,3,4} now i’ve to make a 4×4 i.e n(B)x n(B) i.e cardinal quantity and replenish the field with knowledge such that the information redundancy is 0

here’s one conceivable answer

1    3    4    2
2    4    3    1
3    1    2    4
4    2    1    3

right here in the entire 4 horizontal tactics 4 vertical tactics and a couple of lengthy diagonal tactics the information isn’t repeated and completes an answer the place redundancy is lowered i.e. 0

now we could see some other situation the place there may be redundancy

1    2    3    4
2    1    4    3
3    4    1    2
4    3    2    1

right here despite the fact that the information are distinct in 4 horizontal and four vertical route however the knowledge are repeated alongside 2 diagonals

we all know for n =1 , its conceivable answer is 1
for two and three there is not any conceivable answer for lowered redundancy 0
now how are we able to know the conceivable answers the place the lowered redundancy is 0 for n=4

please assist

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