• There are precisely 100 lights in a huge room.
• A switch panel outside the room has 100 switches each corresponding to one light in the room.
• None of the switches or lights are labeled, so its extremely difficult to identify which switches turns on which light.
• Stan is standing outside of the room and his task is to map each switch to its corresponding light using a marker pen.
• He has to accomplish this mapping in a minimum number of trips to the room.
• Initially all the lights are turned off.
Determine the minimum number of times Stan needs to enter the room to complete the mapping of each switch to its corresponding light.
Notes:
• To check the state of a light Stan must enter the room. He cannot check it from outside.
• There is nothing related to the heating of a light.
This can be done in no less than 7 entries into the room.
Mark each switch with a consecutive binary number, beginning with 0000001. Use leading zeros so they all have 7 digits.
First turn on all the lights that have a 1 in the first position. Enter the room and put a 1 next to each of the lit bulbs and a zero next to each of the unlit bulbs.
Go back to the switch panel and turn off all the on switches, and turn on the ones that are marked with a 1 in the next consecutive position. Re-enter the room and mark a 1 or zero next to the previously placed mark, again depending on on or off status respectively.
Repeat until all the digits of each binary number are accounted for. That's 7 trips into the room.
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Posted by Charlie
on 2022-11-28 09:09:35 |
solution
