Each counter gets a QR code. Scanning signs that phone in as that department. Other desks can read the ticket. Only the desk that opened it, and Facilities, can change it.
Open a desk
Scan the code at your counter.
Each desk has its own QR code. Hardware posts as Hardware. Paint can read it, but only Hardware and Facilities can change it.
Works in the iPhone and Android browser. After you publish, add it to the home screen, then print the desk codes from Facilities.