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#1 bonanova

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Posted 14 February 2008 - 11:49 AM

Down at Morty's last night, Alex and the boys got
into it again. Alex was busy setting them up ...

You all know how to solve the 3 light bulb problem, I'm
sure of that. And a while ago I asked ya about doing 4,
right? They all nodded in agreement.

OK then, said Alex, try this one.
Now you've got five switches that control five light bulbs.
You can't see the bulbs - they're in a closed room.

You can do anything you want with the switches,
say they're marked 1, 2, 3, 4 and 5, and then you can
go into the room and inspect the bulbs - they'll be
marked A, B, C, D and E.

A pint says you can't match the numbers and letters
correctly.

Since Jamie bet on the problem that had 4 bulbs, he
figured he should be the guinea pig on this one, too.
But before he could speak, and while Davey was busy
stroking his beard, Ian asked for the bet.

Did Ian get his pint?
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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 PolishNorbi

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Posted 14 February 2008 - 04:02 PM

Down at Morty's last night, Alex and the boys got
into it again. Alex was busy setting them up ...

You all know how to solve the 3 light bulb problem, I'm
sure of that. And a while ago I asked ya about doing 4,
right? They all nodded in agreement.

OK then, said Alex, try this one.
Now you've got five switches that control five light bulbs.
You can't see the bulbs - they're in a closed room.

You can do anything you want with the switches,
say they're marked 1, 2, 3, 4 and 5, and then you can
go into the room and inspect the bulbs - they'll be
marked A, B, C, D and E.

A pint says you can't match the numbers and letters
correctly.

Since Jamie bet on the problem that had 4 bulbs, he
figured he should be the guinea pig on this one, too.
But before he could speak, and while Davey was busy
stroking his beard, Ian asked for the bet.

Did Ian get his pint?


Spoiler for Ian's is laughing at the ease.

Edited by PolishNorbi, 14 February 2008 - 04:03 PM.

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#3 Jkyle1980

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Posted 14 February 2008 - 10:15 PM

These problems lie in the fact that at first glance, there are only two categories to place bulbs in: on and off. Therefore one and two switches and bulbs would pose no problem. When three lights and bulbs were brought in, the path to the solution was to figure out another way of distinguishing the lights: warm and not warm. This gives us four total combinations of off and on and warm and cool. Now with five bulbs, we are simply adding in another group: hot. With two different light settings and three heat settings, there are a total of six "positions" a bulb can fall into: cool on, cool off, warm on, warm off, hot on, and hot off.

Someone with the proper electrical knowledge would be able take it another step. Remove the panel of swithes. Introduce something into the wiring that would cause its related bulb to burn out. Now, I am not an electrician and do not know if this would cause some sort of blown fuse and prevent all lights from working or something like that. I'm thinking simply. So now you can add another distinguishing factor: broken filament. This now gives you three additional possibilities.

Cool, on, unbroken
Cool, off, unbroken
Warm, on, unbroken
Warm, off, unbroken
Hot, on, unbroken
Hot, off, unbroken
Cool, off, broken
Warm, off, broken
Hot, off, broken
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#4 bonanova

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Posted 14 February 2008 - 10:29 PM

These problems lie in the fact that at first glance, there are only two categories to place bulbs in: on and off. Therefore one and two switches and bulbs would pose no problem. When three lights and bulbs were brought in, the path to the solution was to figure out another way of distinguishing the lights: warm and not warm. This gives us four total combinations of off and on and warm and cool. Now with five bulbs, we are simply adding in another group: hot. With two different light settings and three heat settings, there are a total of six "positions" a bulb can fall into: cool on, cool off, warm on, warm off, hot on, and hot off.

Someone with the proper electrical knowledge would be able take it another step. Remove the panel of swithes. Introduce something into the wiring that would cause its related bulb to burn out. Now, I am not an electrician and do not know if this would cause some sort of blown fuse and prevent all lights from working or something like that. I'm thinking simply. So now you can add another distinguishing factor: broken filament. This now gives you three additional possibilities.

Cool, on, unbroken
Cool, off, unbroken
Warm, on, unbroken
Warm, off, unbroken
Hot, on, unbroken
Hot, off, unbroken
Cool, off, broken
Warm, off, broken
Hot, off, broken

Wow. All I can say is you're waaaaaaaaaaay out of the box. Bravo. :blink:
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#5 TwoaDay

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Posted 15 February 2008 - 12:57 AM

but could you figure it out for 6 switches?
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#6 Jkyle1980

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Posted 15 February 2008 - 02:48 AM

but could you figure it out for 6 switches?


With my example above, I could do it for 9.
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