#StackBounty: #np-hardness #subset-sum Can we map this problem to subset-sum?

Bounty: 50

Let there be $n$ set of ordered pairs
$s_1={(c_1,f_1),(c_1,f_2) …(c_1,f_m)}$,
$s_2={(c_2,f_1),(c_2,f_2) …(c_2,f_m)}$,
$s_3={(c_3,f_1),(c_3,f_2) …(c_3,f_m)}$,
….
$s_n={(c_n,f_1)(c_n,f_2) …(c_n,f_m)}$

and

$T((c,f))$ be a function that takes an ordered pair or element of the sets and returns a positive rational number.

can we select one element each from all the $n$ sets such that $sum T((c_i,f_j)) =T$ where $bigcap_{i=1}^{n } c_i =phi$


Get this bounty!!!

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