Matematické Fórum

In a building, there is a hexagonal room with one door on each wall. Each door gives way to a different room (six rooms in addition to the hexagonal one). Seen from the interior all of the six rooms are absolutely identical in content and dimension. They are empty except for a light bulb on the ceiling. (All bulbs are identical and have only two states (lit or extinguished). The four walls inside each room are smooth and white with a door on one of the walls opening to the central room. The rooms are completely insulated with nothing leaving the room unless the door is open. (There is no keyhole, no sound escapes, etc..) In front of each door, seen from the central room, is a button (a total of six buttons). There is no interaction between buttons. The hexagonal room is not affected by the action of the buttons; the hexagonal room is not important to the problem. A person must discover the function of each button with regard to its associated room. One does not know beforehand if the light in the room is on or off. (The rooms may be in different states at the beginning). Each button can be actuated only one time and remains blocked thereafter. The person can not actuate the button after having entered a room (that would be too easy). In each room there is a sheet of paper and a pencil; the person must write what is discovered before going out of the room. The doors are marked with a unique number from 1 to 6 and one must start with door 1. A person must approach the first button, press it and enter the room. He then must document the function of that button. He then must leave and approach the second button, press it, enter the second room, and document the function of the second button. He must proceed in this way through the third, the fourth, and the fifth. He must finish with the sixth to complete the task. Given that the explanation for each event will be different and the observations are always correct, what must be the outcome of the sixth button?

Note that the man is alone in the building, and that there is no problem with the electrical power supply in the building.

Mám to iba ako vidíte v anglickom jazyku. Ak by sa niekto našiel, kto by to preložil, bol by som mu nesmierne vďačný..Nemám tušenie, o čom to je, lebo neviem tak dobre po anglicky. Môžete to rovno aj vyriešiť, ale vraj je to ťažké..Ak bude nejasnosť v zadaniach, napíšem tým američanom v čom je problém, ale formulujte to anglicky, lebo ja to prekladať nebudem - neviem :D