A puzzle can have exactly one mathematical solution and still be unpleasant to solve if the only practical route is blind trial-and-error. AllSolveOne treats those as two separate quality questions.
Uniqueness answers “is there only one solution?”
The exact solution counter checks whether a second valid completed grid exists. A production puzzle is rejected if the answer is anything other than exactly one.
The logical solver answers “can we reach it through deductions?”
AllSolveOne also runs a bounded logical solve process. The generated puzzle must be completed by that solver and fall inside the accepted logic-score range.
Why this matters in a live race
Random guessing would make competitive results noisier and less satisfying. A no-guess design means the race rewards reading constraints and executing deductions rather than getting lucky on a branch.
Put the idea into practice
The fastest way to understand the interaction between row, column and cage constraints is to solve a board. Start with the free practice puzzle, then enter the live world when you are ready to race for Discoverer.