Let’s say you are given nine identical-looking eggs and told that one is heavier than the others, but you are not told which one. Fortunately, you have a beam balance for comparing the masses of the eggs. Unfortunately, the balance is a rental, and you are being charged each time you use it. So assuming you are strapped for cash and wish to know which of the nine eggs is heaviest - who wouldn’t? - what is teh minimum number of times you must weigh the eggs in order to find it?
The answer, it may surprise you to learn, is only twice. Here’s how: First divide the eggs into groups of three and compare the masses of two groups; if one trio is heavier, simply compare two eggs from that one and you’re done. (If the two balance, then the third is heavier.) On the other hand, if the two triplets you weighed have the same mass, compare two eggs from the trio you initially left out!
(9-6)-(2+1)=the heavier egg!
Probably wouldn’t surpise you if I told you that out of the 256 students who saw this on the test only 17 got it correct. Then again, it was only a 5% extra credit question on the exam. (Algebra.)
