Progress bars
Suppose we want to run identical programs on a computer. There are 2 progress bars showing the progress of the programs. One shows the progress of the current program and the other shows the total progress ( i.e. there are 6 60-step programs, one progress bar shows Program 1 step 30/60, the other shows 8.33 %). Find a formula for the number of times the first progress bar passes the second one during the entire process ( running all programs )
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1 solution
As the 2nd progress bar only finishes once during the entire process and the 1st finished n times, we see that the bars meet n times. We might be tempted to simply put n as the answer. However, the first time the bars meet is at the starting point, so the 1st bar does not pass the 2nd bar, therefore it is not counted. The same reasoning applies to the last meet, therefore we can conclude that the answer is n − 2 .