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/sci/ - Science & Math

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11869482 No.11869482 [Reply] [Original]

Two people can enter the machine and switch their consciousness. Whenever two people switch their consciousness, the light bulb switches (on->off and off->on). You have access to as many people as you want. The light bulb starts off being off. Is it possible to using the machine in such a way that in the end, everyone's consciouness is back to where it started but the light bulb is on. If yes, give a method how to do it, and if not, explain why.

>> No.11869496

>>11869482
Impossible, if you can only switch two people at a time and the function of the lightbulb is binary (on or off) no matter how many times you switch people around when you bring them to the orginal position the lightbulb will again go back to it's original state, being off.

>> No.11869517 [DELETED] 

>>11869496
The original state is on.
A + A = off
A + B = On
B + B = Off
B + A = On

>> No.11869528

>>11869496
Ok, can you explain why?

>> No.11869531

>>11869482
Literally just retrace whichever steps you take back to the original order

>> No.11869534

>>11869531
Read the question wrong sry

>> No.11869538

a1 + a2 = a2(1) + a1(2) = on
b1 + b2 = b2(1) + b1(2) = off
a1(2) + b2(1) = a(b2(a2)) + b(a1(b1)) = on
a2(1) + b1(2) = a(b1)(a1)) + b(a2(b2)) = off
a(b1)(a1)) + a(b2(a2)) = a1+a2 (original A) = On
b(a1(b1)) + b(a2(b2)) = b1 + b2 (original B) = off

>> No.11869542

>>11869538
Whay do the addition signs mean

>> No.11869552

>>11869482
I think that the answer is no. Let's assume that there are only 2 people - person A with A's consciousness, an person B with B's consciousness. They trade their consciousness. Now we have person A with B's consciousness and persin B with A's consciousness. That's one switch made. The light bulb is on. Now, they trade again. That is another switch, 2 in total. But the light bulb is off again. Now imagine 3 people - A, B and C with their own consciousness. A and B trade, that's one switch. A and C trade, these are 2 swtiches. A and C trade again, 3 switches. A and B trade again, 4 switches. Everybody has their own consciousness back, but still an even number of switches, so the light bulb is still off. And so on. In order for 2 people to trade their own consciousness and then get it back, 2 switches are needed between two same people. The machine allows only 2 people at the time. So for 2 people, it's 2 switches, 3 people 4 switches, 4 people 6 switces and so on. For 1 more person 2 more switches are needed. So the number of switches always stay the same - even. And since an odd number of switches are needed for light to stay on, it always stays off.

>> No.11869562

>>11869538
My math was wrong but the answer is still yes.

>>11869482
>Two people can enter the machine

No where does it say two people MUST enter the machine, nor does it restrict the use of 1 person just flipping the switch. The machine never specified that it wouldnt activate or the light wouldn't turn on just by flipping the switch. Theoretically, you could just have one person flip the switch a couple times and retain his consciousness.

>> No.11869633

>>11869482
I tried it with 7 people in 22 steps, and failed, but I had misconstrued the question again. For me, each body had a light, so 7 lights switching on and off. I could get the people back in their bodies, but the final light had to stay off. Since I had 22 steps, if there was one single light keeping track of every shift, due to the even number that would also be off. For n=2,3,4,5,7 it's a failure but I don't know how I'd generalize that

>> No.11869655
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11869655

Sign of identity permutation is 1. Sign of an odd number of transpositions is -1. Contradiction.

>> No.11869674

>>11869482
x x

>> No.11870460

>>11869562
Yes, but it says that the light switches WHEN two people swap consciousness. Therefore, it is impossible to have the light on with everyone’s consciousness restored

>> No.11870583

>>11869482
Isn't this just the Futurama Theorem?
https://en.m.wikipedia.org/wiki/The_Prisoner_of_Benda

>> No.11870698

0 People, 0 swaps, lights off
Zero is still a valid number

>> No.11871581

>>11869496
Lol brainlet. I'll just place a capacitor in the circuit.

>> No.11871662

>>11869482
All of the matter in the entire universe ends at the bottom of a black hole compressed to a single point. The heat experienced in the moment of this complete compression is immense, which might then explain why the concept of Hell exists. The people who conceived of Hell were extending out to the furthest point of matter, and trying to conceptualize the experience of complete compression which is the destiny of all matter.
Fortunately, sentience only occurs when there are organs working in conjunction, so no one will have to experience such a compression with a sentient mind.

>> No.11872114

>>11869552
>>11869655
This reminds me of Euler's solution to https://en.m.wikipedia.org/wiki/Seven_Bridges_of_K%C3%B6nigsberg (I guess the opposite/inverse of it, more precisely)