Question 1
There are $N$ untidy employees in an office, each with a pile of rubbish on their desk. They leave for lunch one at a time, each only after the preceding employee returns. Whenever an employee leaves, every other employee puts half of the rubbish on their own desk onto the absent employee’s desk. Is it possible that, after everyone has had lunch, every desk has exactly its initial amount of rubbish, if (a) $N=2$; (b) $N=10$? Original weights: (a) 1 point, (b) 3 points.
