Puzzle of the Week for 11 January 1999

You have just invented a device that will revolutionize life in the 21st century: a drill bit that can make square holes! You need to determine how fast your bit can be used safely. Your test apparatus can turn your bit at any multiple of 100 revolutions per minute (rpm) up to 6000 rpm, while it drills a square hole into a block of test material. (If the bit can be used safely at 6000 rpm, it's not necessary to test it at higher speeds.) If you make a test at a speed that is too high, your bit will be destroyed, and you have only two of them. It costs $10 for materials to perform each test. What strategy for testing will cost the least in the worst case, and how much will it cost? How would the answer change if you could make additional bits for testing for $10 each?