SOLUTION IF #9 IS EITHER HEAVY OR LIGHT

 

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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