Here is solution if Unique Weight was number 9 and Heavy

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 weight is either 9 10 11 or 12

Weigh #2

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

Solver would see that Left side is Heavy

So Unique weight must be either 9 is Heavy or 11 or 12 is Light

Weigh#3

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

Solver would see scale is in balance so Unique weight is 9 Heavy

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Now assume instead that 9 is Light

Weigh#1

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

Solver would see scale in balance so Unique is either 9 10 11 or 12

Weigh#2

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

Solver would see that Left is Light so either 9 is Light or 11 or 12 is Heavy

Weigh #3

Place 11 on Left and Place 12 on Right

Solver would see scale is in balance so Unique weight is 9 and it is Light

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