I used 5 colors.

For changing colors I used the invisible join.

Using US terms:

Color A:
Start with a magic ring, secure, make 2 slip stitches (=1dc), another 11dc in the ring (=12st.).

Color B:
2dc in every stitch (=24st.).
Next round: after closing the previous round, make 3 slip stitches (=1dc), 2dc in the next stitch, 1dc repeat from * to * (=36st.).

Color C:
1sc in every stitch (=36st.)
No increases, the coaster will curl up.

Color D:
adding another 12st.: 1dc, 1dc, 2dc in the next stitch (=48st.)

Color A:
1hdc in every stitch.
No increases in this round. It will curl up even further (and no, it’s not going to be a basket).

Color E:
repeat: 1sc, in the next stitch: 1hdc, 2dc, 1hdc.
All the curliness will disappear.