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The pairs of matching numbers can each be connected by a single path within the upper grid (as in the free iPhone game Flow). Once the grid is filled in with the paths of numbers, use an appropriate rotation cypher on the letters in the lower grid to reveal the message:

W   E   L   L   I   S   U   P   P
O   S   E   Y   O   U   H   A   V
E   S   O   L   V   E   D   T   H
I   S   P   U   Z   Z   L   E   H
E   A   D   T   O   T   H   E   A
R   T   M   U   S   E   U   M   L
A   K   E   T   O   C   L   A   I
M   Y   O   U   R   P   R   I   Z
E   F   A   R   E   W   E   L   L

The solution is illustrated in this spreadsheet.

The badge could be found next to the lake at the AU art museum.

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