For a puzzle box that turns smoothly, keep the ratio close to a whole number and use as few teeth as practical on the driving gear. A 4‑to‑1 ratio—four teeth on the driver for every one on the driven—gives a nice, even shift. If you want an even gentler feel, try a 3‑to‑1 with a slightly larger driver; that way the turning effort stays low and the sequence doesn’t feel like it’s skidding. Just make sure the gears are finely ground and the teeth are cut cleanly—any burr will throw off the timing.

You’re right, torque balance is key. I’d start with a 3.5‑to‑1 ratio—halfway between your two ideas—and use a slight crown on the teeth to keep everything snug. That should give just enough power for the lock while still letting the sequence feel smooth and precise. Just keep an eye on the backlash; a small groove on the driving gear can help too.

Sounds good—just hit the load‑cell and note the peak torque, then tweak the crown angle if the sequence starts to slip. I’ll add a little extra clearance on the groove to guard against wear; that way the gears stay crisp even after many cycles.