Each lock is a 'how many ways?' puzzle. Count the possibilities correctly to crack it, guess wrong and the alarm costs you ten seconds.
Work down a vault of combinatorics locks, each asking how many ways something can happen. Pick the right count from the options to open the lock and move on. Wrong picks add a time penalty and briefly lock you out, so accuracy beats guessing. Crack the whole vault as fast as you can.
Counting Cards is a combinatorics puzzle that drills permutations, combinations and the multiplication principle.
"How many ways can this happen" is the central question of combinatorics, and the locks here run through its standard forms — arrangements, selections, and the difference between them.
Presenting each as a lock with a single numeric answer is the original framing.
The difficulty in counting problems is almost never the arithmetic. It is deciding whether order matters and whether repetition is allowed, because those two questions pick which formula applies — and a confident wrong answer usually comes from answering them without noticing you did.
Counting Cards is a timed combinatorics puzzle that drills permutations, combinations and the multiplication principle. It's an original free browser game made for PlayPendium.