Question

A hexomino is a planar figure formed by connecting six unit squares such that adjacent squares share a common side. One possible hexomino is shown. How many distinct hexominoes can be drawn that have exactly four squares in a row? A hexomino is distinct if it cannot be reflected or rotated to form another hexomino.

Answer 1

If we like the hexomino to have exactly 4 squares in a row, then we have possibilities to put the first of the remaining two squares, but since we want distinct hexominoes this reduces to 4.

Once we put the next square, the last one can be put in 5 different places.

Then the total number of hexominoes are 9. To this we have to add four posibilities that can't be reflect on each other.

Therefore, the total number of hexominoes with 4 squares in a row is 13.