April Giveaway 2018

On the image below you can see 11 points in the plane placed in such a way that there exist 6 lines passing through 4 points each. Can you place 10 points in the plane, such that there are 5 lines passing through 4 points each?

CAT = 3, BOWL = 2, FISH = 1. The scratches represent Roman numerals.

4 (CAT with a FISH) + 6 (VI) + 2 (TWO FISH) = 12
1 (FISH) + 2 (BOWL) + 5 (CAT with a BOWL) = 8
5 (CAT with a BOWL) + 3 (CAT) + 3 (III) = 11

Therefore, the correct answer is 4 + 2 + 3 = 9.

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saska
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A scip model for solving this puzzle can be found at
https://gist.github.com/saska-gist/3d75de703013b3b237ecccc59bb83bba