b You do not have to put it in the right place or orientation.
C
c Does this new pieces have any rotational symmetry.
A
a 180^(∘)
B
b 4 ways
C
c 1 way
Practice makes perfect
a Let's make things easy for us and imagine that the two pieces look like below. Also, since the pieces are identical, we only have to consider one of them when determining it's rotational symmetry.
To turn this piece so that it maps onto itself, we would have to rotate it by 180^(∘) like below.
Therefore, the rotational symmetry of both pieces are 180^(∘).
b We can put the piece in the correct spot and with the correct orientation. But given the rotational symmetry we can rotate it 180^(∘) and it would still fit. That's two ways we can fit it in the puzzle. Additionally, we can put it in the incorrect spot, and in two different orientations which gives a total of 4 ways.
c Let's draw the pieces when put together.
We cannot rotate this larger piece and still make it fit in the puzzle. Therefore, there is only one way we can make it fit.
