Here is the solution if the unique weight is number 3 and it is Lighter
than all others, followed by solution if it was Heavy.

1st weigh

Solver would place 1 2 3 & 4 on left side of scale and 5 6 7 8 on right side.
He now knows unique weight is either 1 2 3 or 4 as Light
OR 5 6 7 or 8 as Heavy

You and I know that 3 is Light.

2nd weigh

Solver now places 1 2 & 6 on left side of scale and 3 4 & 5 on right side.
The left side is Heavy OR right side is Light (WE know 3 is Light)
It must be either 1 or 2 or 6 as Heavy or 3, 4 or 5 as Light.

It cannot be 1 or 2 Heavy---See Weigh #1 results

It cannot be 5 as Light-----See Weigh #1 results

It must be 6 is Heavy or either 3 or 4 is Light

3rd weigh

Place 3 on Left and 4 on Right
Left side is Light so 6 is a Standard Weight
It cannot be 4 as Heavy (see Weigh #1 data)
It must be that 3 is Light (the Unique weight
**********

NOW WE ASSUME YOU SELECTED NUMBER 3 AS BEING HEAVY INSTEAD OF LIGHT.

1st Weigh

Solver would place 1 2 3 and 4 on Left side of scale and 5 6 7 and 8 on Right side of scale.
Left side would be Heavy so it is either 1 2 3 4 as Heavy or 5 6 7 or 8 as Light.

2nd weigh

Solver would place 1 2 6 on left side of scale and 3 4 5 on right side.

Either Left side holds a Light or Right side holds a Heavy(WE know 3 is Heavy)
Unique weight is either 1 2 or 6 Light or 3 4 or 5 Heavy.

3rd Weigh

Place 3 on Left and Place 4 on Right

Either 3 is Heavy or 4 is Light
Cant be 4 is Light (see earlier data results)
So 3 is Heavy

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