You might need to get out a ball of wool or two to find this solution. The stitch markers will give you and your needles and wool some pointers.
You'll have to cast on 47 stitches before you're ready to start row 1. Then the question is what to knit and what to purl in what colour, and what's the difference when you look at it anyway?
All odd rows are (flat) knits on the right side. For even rows your knitting is turned over, so not only are you knitting in the other direction, your knits will be (raised) purls and your purls will be (flat) knits. It is the raised black purls and the flat white knits that are going to reveal the illusion in your knitting.