FUTILITY
grasp at straws
to depend on something that is useless; to make a futile attempt at something.John couldn't answer the teacher's question. He was just grasping at straws.There I was, grasping at straws, with no one to help me.
lead someone on a merry chase
to lead someone in a purposeless pursuit.What a waste of time. You really led me on a merry chase.Jane led Bill on a merry chase trying to find an antique lamp.
on a fool's errand
involved in a useless journey or task.Bill went for an interview, but he was on a fool's errand. The job had already been filled.I was sent on a fool's errand to buy some flowers. I knew the shop would be closed by then.
wild-goose chase
a worthless hunt or chase; a futile pursuit.I wasted all afternoon on a wild-goose chase.John was angry because he was sent out on a wild-goose chase.