100 showers
In front of a swimming pool there are 100 showers. But the plumber did something wrong. When you turn on your shower then you activate exactly 5 other showers as well.
It is always possible to choose 10 showers and close the other 90, so that the customers don't notice the defect.
True or False? Prove your answer!
Source: First round of the German Mathmatical Olympiad 2010/2011 for eleventh graders (German PDF)
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