The Scarborough-Stone Problem asks whether the product of any family of sequentially compact spaces is always countably compact. Consistently no, but whether it may have a consistent positive answer remains open. The special case asking whether a separable sequentially compact space has all powers countably compact has, it seems, not been previously studied. We present a consistent counterexample and some related results toward a possible positive solution.

This is joint work with César Corral and Alan Dow.