Definition
Impossibility
Impossibility means that no object, value, or arrangement can satisfy all the conditions.
What it means
Not finding an answer is not enough. To prove impossibility, show why every possible answer must break at least one rule.
Remember it
Every path reaches a blocked gate.
Example
An odd number of identical counters cannot be split into two equal whole-number groups. If each group had k counters, the total would be 2k, which is even. That contradicts the total being odd, so the split is impossible.
Watch for
A hard problem is not an impossible problem. “I could not find one” does not rule out every possible solution.
Common mix-up
Existence needs at least one working case. Impossibility needs a reason that no case can work.
Exact meaning
An impossibility claim says that there is no object, value, case, or arrangement satisfying every stated requirement. It must be established by reasoning that rules out all possibilities, not merely by an unsuccessful search.