A useless search or effort with little chance of success, ultimately resulting in wasted time.
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A search or an effort that wastes time because it leads nowhere.
When you go on a wild goose chase, you chase something you'll never find.
It's often used when someone is sent the wrong way or follows a bad lead.
"Fool's Errand"
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A task that is completely pointless from the very beginning
"Chasing Rainbows"
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Pursuing impossible or unrealistic dreams that can never be achieved
"Wild Goose Chase"
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A time-wasting search that leads nowhere, often due to misleading information