head-scratcher

noun2

1. •
   A device used to scratch the head.

   • Her aunt's husband or her grandfather brings a head scratcher. "If the maid scratched her hair or body with her fingers during these days of observance, her hair would fall out." — 2004
2. •
   (informal, figurative) Something particularly puzzling or confusing.

   • Golden Globes nominations a head-scratcher — 2007