>>11518018Weigh 1234 vs 5678
will either be equal or not - 2 scenarios
1st scenario - if equal 12345678 are control - weigh 9 10 11 vs 1 2 3. if equal, 12 is odd one out, weigh 12 against a control to see if heavier or lighter.
if not, lets say 9 10 11 are heavier than the control. now weigh 9 vs 10 - if equal, know 11 is heavier. if uneven, the heavier of the 9 or 10 is the odd one out.
2nd scenario - lets say that 1234 are heavier, and 5678 are lighter. 9 10 11 12 are now the control.
now we weigh 12567 vs 8 9 10 11 12
if 12567 is heavier, then either 1 or 2 is heavier or 8 is lighter. weigh 1 vs 2, if equal then 8 is lighter, if not then heavier of the two is the odd one out
if 12567 is lighter, then one of 5 6 7 is lighter. weigh 5 vs 6, if equal then 7 is lighter, if not then lighter of the two is odd one out
if 12567 and 8 9 10 11 12 are equal, then 3 or 4 is heavier. weigh these against each other to see which is heavier
even though we assumed a group to be heavier, you could switch the labels and still reach the same result
