The following puzzle requires thoughtful analysis for solution. There are 12 weights all with similar appearance. 11 of the 12 are of a Standard weight but 1 of them is of a different weight- we will term it the Unique Weight. It may be Heavier or it may be Lighter than the Standards. You are given a balance scale with the opportunity to make 3 separate weighings and thus determine which is the Unique Weight.
The construction of the 1st weighing is crucial to the solution. There are 36 possible conditions. Weight number 1 may be Heavy or Light or Standard, weight number 2 may be Heavy or Light or Standard , same for number 3, 4 etc.
The IMPORTANT first weigh is as follows:
If you were to place 1 2 3 and 4 on one side(for example the Left) and 5 6 7 8 on the other side (which would be the Right), 3 possible conditions would be possible.
Scale in balance
So the results of the VERY FIRST WEIGH determine the nature of the 2nd weigh. The results of the second weigh determine the nature of the third weigh
Please carefully take note of the following: Remember, if a certain numbered weight has been identified as a POSSIBLE CANDIDATE for being the Unique Weight,and might be, for example, a POSSIBLE Light, then in subsequent weighings it is NOT POSSIBLE for it to be a POSSIBLE candidate for a HEAVY weight. What does this mean? It means that since it CANNOT be a POSSIBLE candidate for LIGHT in one weigh and then HEAVY in a different weigh, it is definitely a STANDARD, a vital piece of information. So in gathering information from the CURRENT weigh, be sure to consider information obtained from previous weighings.