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Light bulb problem on steroids


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6 replies to this topic

#1 bonanova

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Posted 18 September 2007 - 08:27 AM

In a room are 100 light bulbs, numbered 1 to 100.
Outside the room are 100 switches, numbered 1 to 100. Each switch controls its same-numbered bulb.
Initially, all the switches are off.

100 people, numbered 1 to 100, are asked to flip some or all of the switches.
"Flip" means "change its state" - if it's on, turn it off; if it's off, turn it on.

Person 1 must flip every switch: 1, 2, 3, ..., 97, 98, 99, 100.
Person 2 must flip every 2nd switch: 2, 4, 6, ..., 96, 98, 100.
Person 3 must flip every 3rd switch: 3, 6, 9, ..., 93, 96, 99.
------
Person 15 must flip every 15th switch: 15, 30, 45, 60, 75, 90.
------
Person 99 must flip every 99th switch: 99.
Person 100 must flip every 100th switch: 100.

When each person has flipped his/her assigned switches, s/he leaves.
Finally, you enter the room to check the bulbs.

Assuming the 100 people did as they were instructed:

[1] are any bulbs lit?
[2] if not, why not?
[3] if so, which one[s]?

Spoiler for Hints

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#2 KamZhiYhi

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Posted 18 September 2007 - 01:31 PM

I can say for sure that light bulb number 1 is on. But im not sure, or just not bothered to try to work out the rest
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#3 unreality

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Posted 18 September 2007 - 09:52 PM

In a room are 100 light bulbs, numbered 1 to 100.
Outside the room are 100 switches, numbered 1 to 100. Each switch controls its same-numbered bulb.
Initially, all the switches are off.

100 people, numbered 1 to 100, are asked to flip some or all of the switches.
"Flip" means "change its state" - if it's on, turn it off; if it's off, turn it on.

Person 1 must flip every switch: 1, 2, 3, ..., 97, 98, 99, 100.
Person 2 must flip every 2nd switch: 2, 4, 6, ..., 96, 98, 100.
Person 3 must flip every 3rd switch: 3, 6, 9, ..., 93, 96, 99.
------
Person 15 must flip every 15th switch: 15, 30, 45, 60, 75, 90.
------
Person 99 must flip every 99th switch: 99.
Person 100 must flip every 100th switch: 100.

When each person has flipped his/her assigned switches, s/he leaves.
Finally, you enter the room to check the bulbs.

Assuming the 100 people did as they were instructed:

[1] are any bulbs lit?
[2] if not, why not?
[3] if so, which one[s]?




Spoiler for ...

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#4 Michlips

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Posted 19 September 2007 - 01:22 AM

Bonanova:

What the HECK is the answer?!?!

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#5 Martini

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Posted 19 September 2007 - 01:29 AM

Welcome to the boards, Michlips. It's customary for the OP to give people time to figure the answer out and for others to discuss their rationale for their answer and sometimes their rationale for why others are wrong. It makes things a little more interesting. After all, what's the rush?
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#6 bonanova

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Posted 19 September 2007 - 08:17 AM

You can pose this puzzle with 10 bulbs instead of with 100.
But then it's too easy to grind it out; boring.

You can also pose it with 1000 bulbs.
But life is short, and people with any sense walk away, and miss the fun.
Michlips appears to be in that [sensible <!-- s;) --><!-- s;) --> ] group.

The whole idea is to find the short cut; and grinding it out partially can light the way.
ergo, 100 bulbs is only moderately complex and sucks you in to the search.

KamZhiYhi took the first step and realized bulb #1 would be on - partial credit.
unreality went farther, saw the pattern, and found the answer.

Here's another way to see the solution.
Spoiler for ...

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#7 eedray

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Posted 27 September 2007 - 11:59 AM

pretty cool puzzle
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