Why Every Good Puzzle Has Exactly One Solution

Try this thought experiment: you solve a puzzle correctly, check the answer, and it says you are wrong because the author had a different valid solution in mind. Nothing you could have deduced would have told you. That is why serious puzzle makers insist on uniqueness.

How a puzzle gets checked

A puzzle generator usually works backwards. You build a finished board first (the "planted" solution), then hide information: remove numbers or draw region borders to leave only the clues. After each change a solver counts the solutions. If there is more than one, the puzzle is rejected or given another clue.

For a small board, the solver can simply try everything with backtracking: choose a square, shade it or not, discard any branch that already breaks a rule, and count the boards that survive.

Difficulty is a separate question

Having one solution does not make a puzzle easy or hard. A computer can crunch through a board far faster than a person, so difficulty is usually graded by how many kinds of reasoning a human needs: whether simple patterns are enough, or whether chains of "if this, then that" are required. That is why the same 10x10 can feel gentle or fiendish depending on how the clues are placed.

What this means when you solve

You may rely on the only one solution guarantee. If two squares seem equally good, keep looking - there's a solution nearby.