Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem K. 79. (March 2006)

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 pont)

Deadline expired on April 10, 2006.

Sorry, the solution is available only in Hungarian. Google translation

Megoldás: Például az alábbi szoba megfelel:

### Statistics:

 109 students sent a solution. 6 points: 95 students. 4 points: 5 students. 0 point: 8 students. Unfair, not evaluated: 1 solution.

Problems in Mathematics of KöMaL, March 2006