# Combinatorics problem

Consider a $$4$$-dimensional array $$R$$. Any element of the array can be represented by $$R_{abcd}$$ where $$a,b,c,d$$ are any four (not necessarily distinct) integers from the set $$\{1,2,3…N\}$$.

Given that,

i) $$R_{abcd}=-R_{abdc}$$

ii) $$R_{abcd}=-R_{bacd}$$

iii) $$R_{abcd}=R_{cdab}$$

iv) $$R_{abcd}+R_{adbc}+R_{acdb}=0$$

When $$N=15$$, how many elements of $$R$$ are independent?

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