The puzzle is as follows:
Assume that you have a two pan scale and three weights, one of 1 pound, the other 3 pounds and the last one 9 pounds. How many objects of different weights can you weigh at maximum, using just these 3 weights ?
We can measure 6 pounds by keeping the 3 pound weight and the 6 pound object on one pan and the 9 pound weight on the other pan.
We can measure 4 pounds by keeping the 3 pounds and 1 pound weights on one pan and the 4 pound object on the other pan, etc.
The choices given are:
- 10 objects
- 12 objects
- 13 objects
- 14 objects
This puzzle appears to be an adaptation from a reprinted copy of an intelligence psychometry JPA exam of the late 1990s which might be based on Weschler IQ tests from that time period, a similar problem has been also used in Thurstone's exams of the 1960s.
I assume that a strategy to solve this puzzle is to find the possible weights that we can have with all these weights combined.
Assuming that we use the 1 pound weight, we can only measure one object.
Using the 1 pound and/or 3 pound weight, we can measure:
2, 3 and 4 pounds. Thus there are three additional objects.
Using the 1 pound and/or 3 pound and/or 9 pound weight:
5, 6, 7, 8, 9, 10, 11, 12 pounds objects
This accounts for 8 additional objects.
If we add all these up:
Therefore choice 2 would be correct
I'm not sure if this is the right answer, but to me is the answer with the most logical sense to me. But I could be wrong. Could someone else help me?