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100 Lights and 100 Switches (Posted on 2022-11-28) Difficulty: 3 of 5
• 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.

• 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.

See The Solution Submitted by K Sengupta    
Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution solution | Comment 2 of 6 |
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.

  Posted by Charlie on 2022-11-28 09:09:35
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