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bonanova

Covering triangles with triminoes

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6: no - after putting a triangle in each corner (which must be done to fill the corners), you must put another triangle with its edge along the edge of the board, which then leaves you with 3 separated hexagons left
7: no - 28 hexagons on the board is not divisible by 3

8: no - again, after putting the triangles in the corners, you will end up with 3 hexagons that left over that can't be covered with a triangle

9: yes

 

I can give more detail if needed for any of these...but the OP didn't actually ask for "why or why not..." so...

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