I'm a big nerd. Here's a problem for all you other nerds out there.
We have 25 balls of different weights. We would like to find out which are the 5 heaviest in order. In other words, we would like to know which ball is the heaviest, 2nd heaviest, 3rd heaviest, 4th heaviest, and 5th heaviest. The only tool we have available to conduct any measurements on these balls is what I'm calling a Relative Weighing device.
This device allows up to 5 balls to be loaded into it one at a time. Once all the balls are inserted, you press a button and the device prints out the ball order that corresponds to heaviest to lightest. As soon as the button is pushed, the device's memory is cleared and all you have is the printout.
For example: Say that you put in Balls 1 through 5 into the machine in that order. The Relative Weighing device might return 3, 4, 2, 1, 5 to indicate that Ball 3 is heavier than Ball 4 is heavier than Ball 2, and so on.
Now, for the question: What is the fewest weigh-ins using our special device to determine the 5 heaviest balls in order?