That scarf is knit, purl, knit, purl all the way across, then you would do the opposite when you flip it around (so, purl, knit, purl knit) so that the ribbing stays the same on both sides..
Ok so here's that exact pattern from what I can tell..
Cast on 19 stitches
Row 1: *knit, purl* repeat from * to * 9 times, knit 1
Row 2 *purl, knit* repeat from * to * 9 times, purl 1
Repeat rows to desired length.
The key is that if you knitted it on one row, you purl it on the next