blind alley
blind alley {n.}
1. A narrow street that has only one entrance and no exit.
The blind alley ended in a brick wall.
2. A way of acting that leads to no good results.
John did not take the job because it was a blind alley.
Tom thought of a way to do the algebra problem, but he found it was a blind alley.
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Source: A Dictionary of American Idioms