Here is the solution if the unique weight is number 11 and it is Heavy.

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

Place 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

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Since Left side is Heavy, he knows that Unique is 11 Heavy

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Now assume instead that 11 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

Place 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

Place 11 on Left and Place 12 on Right.

Left side is a possible Light (see Weigh#2 conclusions)

Right side a possible Heavy ? NO-cannot be(see Weigh#2 conclusions)

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