**B. 4313.** *A*, *B*, *C*, *D*, *E* and *F* are a group of six people. *n* bars of chocolate given to the group in the following way: Everyone gets at least one, *A* gets less than *B*, *B* gets less than *C*, *C* gets less than *D*, *D* gets less than *E*, and finally, *F* gets the most. The members of the group know these conditions, they know the value of *n*, and of course, they know how many bars of chocolate they were given themselves. They have no other information available for them. What is the smallest possible value of *n* for which it is possible to give them the bars of chocolate so that no one can tell how many bars of chocolate everyone has?

Based on a Kavics Kupa competition problem, 2010

(3 points)

**K. 273.** There is a mouse in a long straight tube, at 3/8 of the length. A cat is sitting at a point along the extension of the line of the tube, closer to the end of the tube that the mouse is also closer to. The cat notices the mouse, and starts to run towards the tube. At the same instant, the mouse also starts to run towards one of the ends of the tube. (Both of them run at uniform speeds.) However, the mouse cannot escape: No matter which end of the tube he chooses, the cat will just catch him at the endpoint of the tube. By what factor does the cat run faster than the mouse?

(6 points)

This problem is for grade 9 students only.

**K. 275.** A flying saucer with aliens on board is travelling at a uniform altitude above the ground (that is, at a constant distance from the Earth) at a uniform speed of 800 km/h. At 8 a.m., it was over London, and after 1 hour and 24 minutes it is already over Berlin. Assume that the Earth is a sphere of radius 6370 km. The distance between London and Berlin is 929 km measured along the surface. The saucer travels the shortest path between the two points under the given conditions. Calculate its distance from the surface of the Earth.

(6 points)

This problem is for grade 9 students only.