OK, hang on to your booleans.
Ist Go.....
Divide the balls into groups of 4
Put one group on each side of the scales and the remaining one leave to one side.
3 things can happen:
Balance: All the balls on the scale are equal and the odd one must be in the
unweighed group -> go to 2nd Go/condition 1
Left side up: One of the 4 balls on the left is light or one of the 4 balls on the
right is heavy-> go to 2nd Go/condition 2.
Left side down: One of the 4 balls on the right is light or one of the 4 balls on the
left is heavy-> go to 2nd Go/condition 3
###############################################
2nd Go......
condition 1
You know that all the balls on the scales are equal and the odd one is in the unweighed group. I'll call
the unweighed ones unknowns and the weighed ones standard.
Put 3 unknowns on the left side of the scales and 3 standards on the right.
3 things can happen:
Balance: You know that the odd ball is the remaining unknown. You have cracked the case in 2 goes.
Left side down: You know one of the 3 balls on the left is a possible heavy. -> go to 3rd Go/condition 2
Left side up: You know one of the 3 balls on the left is a possible light. -> go to 3rd Go/condition 2
condition 2
Put two possible heavy ones and one possible light one on the left side and a possible heavy, a possible
light and a known standard one on the right. This leaves two posible lights and a possible heavy on the side
3 things can happen:
Balance: The odd ball is one of the balls on the side. -> go to 3rd Go/condition 4
Left side down: The odd ball is one of the left two possible heavys or the right possible light. -> go to 3rd Go/condition 5
Left side up: The odd ball is either the right possible heavy or the left possible light. -> go to 3rd Go/condition 6
###############################################
3rd Go........
condition 1 Already solved it
condition 2 You know one of the left balls is heavy. Compare any 2.
3 things can happen:
Balance: > The other one is the odd ball
Left side down > The left one is the odd ball
Left side up > The right one is the odd ball
condition 3 You know one of the left balls is light. Compare any 2.
3 things can happen:
Balance: > The other one is the odd ball
Left side down > The right one is the odd ball
Left side up > The left one is the odd ball
condition 4 Compare two of the previously unweighed possible lights.
3 things can happen:
Balance: >The odd ball is the other unweighed one (heavier)
Left side down > The right one is the odd ball(lighter)
Left side up > The left one is the odd ball(lighter)
condition 5 Compare two of the previously unweighed possible heavys.
3 things can happen:
Balance: >The odd ball is the other unweighed one (lighter)
Left side down > The left one is the odd ball(heavier)
Left side up > The right one is the odd ball(heavier)
condition 6 Compare one of the possible heavys (on left) with a known standard ball(on right).
3 things can happen:
Balance: >The odd ball is the other unweighed possible light one (lighter)
Left side down > The odd ball is the possible heavy on the scale(heavier)
Left side up > can't happen
My brain hurts.