Here is solution if Unique Weight was number 12 and Heavy

(followed by solution if it was Light).

Weigh #1

Place 1 2 3 4 on Left and Place 5 6 7 8 on Right

Scale would be in balance so Solver knows Unique is either 9 10 11 or 12

Weigh #2

1 and 9 on Left Place 11 and 12 on Right

Left side would be POSSIBLE 9 as Light or POSSIBLE 11 or 12 as Heavy

Weigh#3

Solver would place Place 11 on Left and Place 12 on Right

Previous weigh shows that if Unique Weight is 11 or 12 it must be Heavy

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Now assume instead that 12 is Light

Weigh #1

Place 1 2 3 4 on Left Place 5 6 7 8 on Right

Scale would be in balance so Solver knows Unique is either 9 10 11 or 12

Weigh #2

1 and 9 on Left and Place 11 and 12 on Right.

This indicates POSSIBLE 9 as Heavy OR possible 11 OR 12 as Light.

Weigh#3

NOTE-after weigh #2 solver knows the Unique is either 11 as Light or 12 as Light

Place 11 on Left and Place 12 on Right to determine which side is Light.

Left side is Light so Unique weight is 11 Light

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