Logic problem?

For the first weighing let us put on the left objects

1,2,3,4 and on the right objects 5,6,7,8.

There are two possibilities. Either they balance, or they don't. If

they balance, then the object is in the group 9,10,11,12. So for

our second weighing, we would put 1,2 in the left pan and 9,10 on the

right. If these balance then the object is either 11 or 12.

Weigh object 1 against 11. If they balance, the object is number 12.

If they do not balance, then 11 is the object.

If 1,2 vs 9,10 do not balance, then the object is either 9 or 10.

Again, weigh 1 against 9. If they balance, the object is number

10, otherwise it is number 9.

That was the easy part.

What if the first weighing 1,2,3,4 vs 5,6,7,8 does not balance? Then

any one of these objects could be the object. Now, in order to

proceed, we must keep track of which side is heavy for each of the

following weighings.

Suppose that 5,6,7,8 is the heavy side. We now weigh 1,5,6 against

2,7,8. If they balance, then the object is either 3 or 4.

Weigh 4 against 9, a known wrong object. If they balance, then the object is 3, otherwise it is 4.

Now, if 1,5,6 vs 2,7,8 does not balance, and 2,7,8 is the heavy side,

then either 7 or 8 is the heavy object, or 1 is a light object.

For the third weighing, weigh 7 against 8. Whichever side is heavy is

the object. If they balance, then 1 is the object. Should the

weighing of 1,5, 6 vs 2,7,8 show 1,5,6 to be the heavy side, then

either 5 or 6 is a heavy object or 2 is a light object. Weigh 5

against 6. The heavier one is the object. If they balance, then 2

is a light object.

First weighing: Compare 4 objects against 4 objects.

If they balance, then all 8 are normal and the different one is in the remaining group of 4.

  Second weighing: Compare 3 normal objects against 3 from the remaining group of 4.

  If they balance, then the remaining object is different and you are finished (unless you want to determined whether it is lighter or heavier).

  If they do not balance, then you know which group contains the different object AND whether it is lighter or heavier.

    Third weighing: Compare two from this group. If they balance, then the final remaining object is different. If they do not balance, you know which is different because you know whether it is lighter or heavier than a normal object.

If the first weighing is unbalanced, then the remaining group of 4 has all normal objects.

Second weighing: Now you have to keep track of the individual objects as you move them around.

Let the left tray contain the heavier group. Set aside 3 objects from the right tray. Move 3 objects from left tray to right tray. Add 3 normal balls to left tray.

If the trays balance, then the different object is in the group of 3 that were set aside, AND the different object is lighter. Use the third weighing to determine which of the three is lighter.

If the trays are unbalanced AND the left tray is still heavier, then the different object is the one that has been in the left tray for both weighings.

If the trays are unbalance AND the right tray is now heavier, then the different object is one of the three that was moved from left tray to right tray. Use the third weighing to determine which of the three is heavier.

put 6 and 6 on each scale

whichever side is lightest, take the 6 blocks and take 2 of them out and put them somewhere special

then with the remaining 4, put them on the scale 2-2 and whichever one is the lightest put them 1-1 to get the lightest

if withe the remaining 4, the 2-2 balance is equal, take the 2 that you removed and placed in a special place and balance them together to get the lightest :)