You can make the game score based. The final score will be inversely proportionate to the time it took to finish the puzzle (which will make the player want to solve it faster) AND proportionate to how closely they’ve predicted the time it will take them to solve the puzzle. (Solving under the predicted time will give the maximum score for the predicted time, since the player can just wait anyway.)
Example: I guess 10 minutes, solve the puzzle in 8 minutes → I get score for 10 minutes.
Example: I guess 7 minutes, solve the puzzle in 8 minutes → I get score for 8 minutes − 1 minute penalty.
If you notice, I accounted for that. The higher your guess is, the lower your score can be. If I guess 1 minute and finish in 1 minute, I get (let’s say) one million points. If I guess 9999 minutes, then I’ll get the score for 9999 minutes even if I finish sooner, for a score of (let’s say) 2 points.
You can make the game score based. The final score will be inversely proportionate to the time it took to finish the puzzle (which will make the player want to solve it faster) AND proportionate to how closely they’ve predicted the time it will take them to solve the puzzle. (Solving under the predicted time will give the maximum score for the predicted time, since the player can just wait anyway.)
Example: I guess 10 minutes, solve the puzzle in 8 minutes → I get score for 10 minutes. Example: I guess 7 minutes, solve the puzzle in 8 minutes → I get score for 8 minutes − 1 minute penalty.
That works—though there should be a penalty for guessing overtime too—otherwise I’d always just guess 9999 minutes :)
If you notice, I accounted for that. The higher your guess is, the lower your score can be. If I guess 1 minute and finish in 1 minute, I get (let’s say) one million points. If I guess 9999 minutes, then I’ll get the score for 9999 minutes even if I finish sooner, for a score of (let’s say) 2 points.
Ah ok—now I get it.