[bonanova]

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?

[Guest]

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?

Leave 1 off the full time.

Turn 2,3,4 on.

After twenty minutes, turn off 4.

After a few minutes, just enough time for 4 to cool, but not be as cool as if it never turned on. Turn on 5, and turn off 2. And quickly go into the room.

Leaving:

1 = off, cold

2 = off, burning hot.

3 = on, burning hot.

4 = off, not cold, but not hot.

5 = on, but still cool as it hasn't warmed up.

Edited February 14, 2008 by PolishNorbi

[Guest]

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

[bonanova]

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.

[TwoaDay]

but could you figure it out for 6 switches?

[Guest]

but could you figure it out for 6 switches?

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