**B. 3892.** The president of the Pyramid Bank lives in a fancy residential district outside the city. On weekdays, he is driven to the city in a car that leaves the bank in the city at the same time every morning, picks up the president and they arrive at the bank exactly when it opens. One morning, the driver called the president to say that something was wrong with the car and he would be late. So the president left home one hour earlier than usual on foot. Meanwhile, the driver fixed the car and still managed to leave the city at the usual time. He met the bank president on the way, picked him up, and they arrived at the bank 20 minutes before opening. How long did the president walk? (Assume that the speed of the car is constant, and picking up a passenger does not take any time.)

(3 points)

**C. 845.** In an algebra class on the first of April, the students were practising. The task was to simplify the fraction

Agnes, who was the best at mathematics in the class, suggested that if the denominator is not zero, they should just cross out the threes in all the indices, that is, write

Check the result.

(5 points)

**K. 79.** Rob the robot is shut up in a room. He starts moving in one direction and goes on in a straight line until he hits a wall. (A room does not have walls in its interior.) Then he turns to the right and continues in that direction. If he cannot turn right or he would collide in the wall, then he turns left instead and goes on in that direction. If he cannot turn either right or left then he switches himself off. *Figure 1* shows a room in which if Rob starts from position 1, he will go around the room, end up at 1 again, and shut down there. *Figure 2* shows a room in which if Rob starts from either 1 or 2, he will return to the starting point and shut down there. In *Figure 3,* if Rob starts from 1, he will end up at 2, and vice versa, and shut down there. (The grid in the figures is only for making it easier to follow Rob's path.) Draw a room in which there are 4 starting points: If Rob starts at 1, he will end up at 2 and shut down, starting at 2 he will end up at 3 and shut down, starting from 3 he will end up at 1 and shut down, and starting from 4 he will also end up at 4 and shut down.

Figure 1

Figure 2

Figure 3

(6 points)

This problem is for grade 9 students only.