The Burns box pattern is linked to your game installation. It appears there is only one pattern per installation, so if you're playing a second game (or third, etc) on the same device then all players are using the pattern set.
Also, if you play on a second device and buy a Burns box then you're using THAT installation's pattern.
So basically only buy your Burns Boxes on one device.
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edit:
Also, if you re-install, you can not only reset your Burns Box pattern, you could get a new pattern.