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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 $\bigcap_{i=1}^{n } c_i =\phi$

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  • $\begingroup$ I think that the question tries to be that we need to select a transversal, i.e., at most one element from each column. Am I right? $\endgroup$ – domotorp Jul 16 at 16:31
  • $\begingroup$ @domotorp yes that would be one way to put it $\endgroup$ – AVIK DUTTA Jul 16 at 16:35
  • $\begingroup$ Well, I really don't think this question belongs here, it does look too easy. $\endgroup$ – domotorp Jul 16 at 19:57
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This problem is in NP. (easy to verify a given solution)

Subset sum is NP-Complete, so this problem can be reduced to subset sum.

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  • $\begingroup$ Can we really say that there will be a solution =T ? $\endgroup$ – AVIK DUTTA Jul 17 at 17:43

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