A problem can appear impossible because its definition forbids the thing that would solve it.

Sometimes the wall is in the wording. A problem stated with certain conditions built in can rule out, by definition, the very move that would resolve it, and then no amount of ingenuity inside those conditions will help. What looks like a hard problem is a problem plus an unexamined constraint.

List the constraints out loud, including the ones you have never questioned, the ones that came from a habit or somebody’s preference rather than from physics or law. Then ask which of them you are actually required to honour. Problems that have resisted you for months sometimes yield in an afternoon once a single assumed rule turns out to be optional.