I figured out the solution to the puzzler (for some reason I only get the puzzler e-mail every other week, so I’m a bit behind here), but the solution posted is seriously flawed. They state “Clearly, one of the stone pieces has to be one pound” but they don’t give a reason. I started out assuming there was a one pound stone to weigh the one pound amount, but quickly realized that two stones that differed by one pound would also work.

So I turned around and started from the other end of the scale: 40, 39, 38, etc. The only way to measure 39 lbs is if one stone (left off the scale) was 1 lb and 38 lb was 39-1. The most logical way to measure 37 lb was if there was 3 lb stone left off. The only other option was both a 1 lb and a 2 lb stone and it quickly became apparent that there was no way to weight all 40 amounts with 4 pieces. After I had 1 & 3, I guessed the next higher weight was 7 but quickly realized (working from the low end of the weights, 1, 2, 3, etc) that with a 9 lb piece I would be able to measure 5-13 lbs, and that left a 27 lb piece which I checked could make the rest of the measurements. But it isn’t until I had that 3rd stone (9 lb) that the progression 1-3-9-27 was apparent, and at that time the 4th stone’s weight just falls out. But I’m sure that very few people who get 1-3 will figure out "oh, these are powers of 3, the next number must be 9, and, ah ha, that makes the last stone 27, so that has to be the solution. Maybe if there were 5 stones weighing 121 lb, and someone figured out 1-3-9 they might see the pattern and go immediately to 27, but with only 1-3 the pattern really isn’t apparent.

The hint “how would you weigh two pounds?” was worthless. First, they didn’t justify why a stone had to be one lb, then they jumped to the next stone having to be 3 lb since 3-1=2, but *any* two stones that differ by 2 lb could be used for the 2 lb measurement.