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Elections were held in the 45 electoral districts of the United States of Alfagonia. The Green Party won the election in 23 of the 45 districts. Alfagonia is made up of nine states of five districts, each of the states in the shape of a pentomino. According to the Constitution of Alfagonia, the winner of the election is not the party which wins the most districts, but the party which wins the most states.

Given that, based on the Constitution, this particular election was won by the Red Party, is it possible to determine the boundaries between the nine states of the Union?

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    $\begingroup$ Should we assume that the winner of each state is the party that won the majority of the districts? $\endgroup$ – PotatoLatte Nov 24 '20 at 0:45
  • $\begingroup$ Must the pentominoes be distinct? $\endgroup$ – bobble Nov 24 '20 at 3:07
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    $\begingroup$ This seems really underconstrained. $\endgroup$ – xnor Nov 24 '20 at 3:09
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    $\begingroup$ @xnor Perhaps it's a veiled critique of gerrymandering? $\endgroup$ – Paul Panzer Nov 24 '20 at 3:18
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I think this can be achieved easily... I just greedily divide the states and this is one solution I got.

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    $\begingroup$ And it's not hard to see there are a lot of other possible solutions. $\endgroup$ – athin Nov 24 '20 at 0:48
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    $\begingroup$ In that case shoudn't your answer be negative, because you demonstrate it is not possible to determine the boundaries? $\endgroup$ – Paul Panzer Nov 24 '20 at 1:02

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