SOLUTION IF #5 IS EITHER HEAVY OR LIGHT

 

Here is the Solution if the unique weight is number 5 and it is LIGHTER than the others.

1st weigh
Place 1 2 3 and 4 on Left side and Place 5 6 7 8 on Right side.
Left side may be Heavy OR Right side may be Light.

2nd weigh
Place 1 2 and 6 on Left and Place 3 4 and 5 on Right
Left side may contain a Heavy OR Right side may contain a Light.
Can 6 be Heavy? NO Can 3 or 4 be Light? NO
It must be 1 or 2 is Heavy or 5 is Light.

3rd weigh
Place 1 on Left and Place 2 on Right
Scale is IN BALANCE So Weight 5 is the Unique weight and is Light
******** Here is the Solution if the weight number 5 is HEAVY.

1st weigh
Place 1 2 3 and 4 on Left side and Place 5 6 7 and 8 on Right side So Unique weight is either 1 2 3 or 4 being Light or 5 6 7 or 8 being Heavy.

2nd weigh
Place 1 2 and 6 on Left and Place 3 4 and 5 on Right.
Left side is Light OR Right side is Heavy. So Unique Weight is either 1 or 2 is Light OR 5 is Heavy

3rd weigh
Place 1 on Left and Place 2 on Right Scale is in balance. So Unique weight is number 5 as Heavy.

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