there is a puzzle game called The Pedestrian where you control the sign man through signs

Impressive view !

It’s actually a really good question. What you’re explaining is called a collision, by creating the same hash with different numbers you can succesfully login.

This why some standard hashing function become deprecated and are replaced when someone finds a collision. MD5, which was used a lot to hash passwords or files, is considered insecure because of all the collisions people could find.