The human mind is the most fascinating thing in the Universe. Unfortunately, it has its shortcomings, and one of them is that it doesn't handle time lags well. About 15 years ago I ran into a problem that went something like this:
Consider an organization with 1,400 employees; 1,200 are experienced workers, 200 are trainees. Every year 50 experienced workers are retiring. All retirees are always and exclusively replaced by trainees. Promoted trainees are always and exclusively replaced by new hires. It takes four years for a trainee to become an experienced worker. For the last ten years the number of experienced workers has remained constant, when suddenly the number of retirees doubles to 100 and remains at that level. What will happen to the number of experienced workers and the number of trainees? Draw a diagram that shows the number of experienced workers and the number of trainees over time. How confident are you in your prediction?
If you are having a hard time solving this problem, you are not alone. Over the years I have presented it to a number of people, and only a few could solve it with confidence. One person sent me an equation that he had colour-coded with no less than six different colours; it was still wrong and he showed no interest in finding out why.
Other people told me after they couldn't solve the problem that the exercise was not realistic because it ignores resignations, sackings, hiring of experienced workers, and so on. Their logic: If I can't solve a simple problem, why not try a more complex one.