electrical pedantry
I'm sorry, but this is pretty stupid. BoingBoing and Gizmodo think that you can harvest cheap AAA batteries from 9V batteries (the kind with the snaps on top). If you crack open a 9V you'll find six 1.5V cylinders inside, and the 9V battery sells for a much lower price than six AAAs do at retail.
Here are some battery capacities. Let's use the Energizer Industrial Alkaline brand. Their 9Vs have a capacity of 625 milliamp-hours. Their AAAs have a capacity of 1250 milliamp-hours. Watts = volts x amps....
(1.25 amps) x (1.5 volts) x (6 AAA batteries) = 11.25 watts in 6 AAA batteries
(0.625 amps) x (9 volts) x (1 9V battery) = 5.625 watts in one 9V battery
Obviously a 9V and six AAAs aren't actually interchangeable. You can take apart a 9V and get six cylinders with the same voltage as AAA batteries, but nowhere near the same capacity.
A little more arithmetic and you realize that you're getting 6.211 watts per dollar from the AAAs, and 4.199 watts per dollar from the 9V batteries (based on the bulk prices). So this only makes sense for applications where you don't actually care about how much use you'll get out of the battery. For remote controls that you plan to lose before changing the batteries, it might be a good idea (assuming you're ready to carefully crack open a battery). Otherwise, it's not.
The moral: math continues to be useful, and secret battery-industry conspiracies (and free lunches in general) continue to be mostly nonexistent.





Comments
Link to the answer key? At least tell me the ones for the odd-numbered problems are at the back of the archives.
Also, this is very dangerous!
One could get hurt by shorting the cells (or by damaging the seal), causing them to leak or explode. The anode conductor (similar to a small nail) can be ejected with such force that one's eyes could be severely and permanently damaged, not to mention the electrolyte burns. Also, there's much less capacity in one of these compared to a AAA that if completely discharged could also cause an explosive situation.