Assume there is a villiage with 3 houses whose owner's strongly dislike eachother. So they wish to make sure not to run into each other on their daily shopping trips to the four different shops in the villiage. a, can they build a road from every house to every shop such that 2 roads never cross? (roads do not have to be straight) b, what is the maximal number of shops for which the house owners could build non intersecting roads? Justify the answer.

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