Super cool and original opening sequence! I tried playing it a couple of times but the stamping mechanic didn't work reliably for me.
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I played it a couple of times and in the first instance, the stamp went a bit crazy. I think I pushed it too far into the collider below it because it stamped several times in a second. But, did nothing. When I tried it again, it worked for the first sheet of paper, but not the second. So, I'm not exactly sure what was happening.
The multiple stamping doesn't effect the gameplay.
I think it's because I didn't write the instructions clearly. When a worker's performance is too low(indicated by the bar) you have to fire them by throwing them into the bin. The game will wait for you to do that, regardless of if you stamped the to-be-fired employee correctly or not.
Hoped that helped!