donner sa langue au chat

to give up on guessing

This expression means to give up trying to find an answer to a riddle or question.

Allez, je donne ma langue au chat. Quelle est la réponse?

Alright, I give up. What's the answer?

The earlier version was 'jeter sa langue aux chiens' (throw one's tongue to the dogs). Madame de Sévigné helped transform it. The cat replaced the dog because cats were seen as discreet, secret-keeping animals.