[Guest]

In a room, you have 50 switches and 1 Bulb connected to a power source, you have as many wirse as you'd want, how can you pass these wires so that each of the 50 switches if flipped from up to down or from down to up the bulb would change it's status? (on/off)

Here's how the switches work:

Wires can pass through the switch either from up or down, if the switch is flipped up, all the wires passing through up are connected to their opposite ends and all downs are broken, if the switch is down then vice-versa...

Different wires that are passed through the same switch from the same side do not get entangled (as in if Wire A and wire B are connected through the upper side of a switch and the switch is up then A and B are connected to their ends but A is isolated from B)

It is enough that 1 wire to pass through all 50 switches to the bulb to turn it on...

How can this be done?

[Guest]

Could you wire it so that it alternates up, down, up, down, up, etc. for all the switches? So if any one was switched from down to up or vice versa, it would always change the lightbulb's state.

[Guest]

Could you wire it so that it alternates up, down, up, down, up, etc. for all the switches? So if any one was switched from down to up or vice versa, it would always change the lightbulb's state.

But if let's say switch 1 was down then it doesn't matter what all the other switches do it won't light until switch 1 goes up...

You need a system that no matter what the switches' statuses are if you flip any of the 50 switches the bulb will change it's status...

[Guest]

But if let's say switch 1 was down then it doesn't matter what all the other switches do it won't light until switch 1 goes up...

You need a system that no matter what the switches' statuses are if you flip any of the 50 switches the bulb will change it's status...

There's the trivial way that uses 562,949,953,421,312 wires. I assume you're looking for something better though eh?

[Guest]

There's the trivial way that uses 562,949,953,421,312 wires. I assume you're looking for something better though eh?

Actually that's the one, now explain it...

[superprismatic]

Here's how to do it with 2⁴⁹ wires:

Let's make it so that any state of the switches

with an odd number of them in the 'up' state will

light the bulb. So, all configurations with an even

number in the 'up' state will not make the bulb light.

For each of the odd number up states run a wire thru

the up portions of the up switches and thru the down

portions of the down switches. So, you insure that

that any particular wire is live for precisely one

configuration of the switches (and where there are

an odd number them in the 'up' state).

Is this optimal? That is, can fewer wires satisfy

the OP?

[Guest]

Here's how to do it with 2⁴⁹ wires:

Let's make it so that any state of the switches

with an odd number of them in the 'up' state will

light the bulb. So, all configurations with an even

number in the 'up' state will not make the bulb light.

For each of the odd number up states run a wire thru

the up portions of the up switches and thru the down

portions of the down switches. So, you insure that

that any particular wire is live for precisely one

configuration of the switches (and where there are

an odd number them in the 'up' state).

Is this optimal? That is, can fewer wires satisfy

the OP?

Yeah, that is the one, I guess I exaggerated a bit when I made it 50 switches, we have that kind of system in a few places in our house (but only with two switches) and as a kid I pondered for hours thinking how could it work and when I finally figured it out I thought for even more hours thinking how could it be done with more switches, I guess it would be more practical if it were 5 switches or less (for which you'll need 16 wires)...