Authors: Yatsenko I.V., Shapovelov A.V.

All taverns in the kingdom belong to three firms. In an effort to combat monopolies, King Pea issued the following decree: every day, if a certain firm has more than half of all taverns and the number of its taverns is divisible by 5, then this firm retains only one-fifth of its taverns, and the rest are closed. Could it happen that after three days, all firms have fewer taverns? (No new taverns can open during this time.)

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Let's consider an example. Suppose initially the firms have 60, 35, 20 taverns respectively. Then on the first day, the first firm will lose 48 taverns, leaving 12, 35, 20 taverns. On the second day, the second firm will lose 28 taverns, leaving 12, 7, 20 taverns. Finally, on the third day, the third firm will lose 16 taverns.

Note. There are many other examples.

## Answer

Yes, it could.