I am not very religious but sometimes I pray if I have some "unsolvable" problem... No idea if it helps but it feels good to know that maybe "someone" will help me. I do this usually after day long debugging or problem solving without any result, right before bed.
But here are some non logical ways: - reframing - ignoring/delaying - accepting - praying - delegating
Or what the stoic/religion used to say
God, grant me the serenity to accept the things I cannot change, the courage to change the things I can, and the wisdom to know the difference.
P.s I ain't religious or superstition but there is some wisdom in those teachings.
Now in the context of a project if you really can't find any solution, then document and communicate your findings until the budget runs out..