This is a somewhat unusual problem from Presh Talwalkar.  It involves proving a student’s homework problem is impossible.

“I came across a homework problem described as “scary” on Reddit AskMath. You need to fill in the number sentences using the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 exactly once.

You should try a few possibilities to see why this is a challenging question. And do not waste too much time because the exercise is literally impossible!  The challenge is, can you prove no solution exists?”

See Impossible Homework for a solution.