Today our physics teacher teach us how to find resistance of a network of resistance that is messed to heavily(example all sides of a cube are resistance find resistance). Ok those are very good methods, but it seems that they are not result of experiments done by genius persons it seems that they are derived from Kirchoff's laws of loops. Can you please tell me the proof or something like this for their tricks these short cut tricks.
these short ct tricks are

I don't ask him(teacher) for these proofs/derivations because like every time he will say " Proofs never come in examination so what's gain of learning those proofs or derivations."
After all i hope you will not reply so.

thanks for reading. make reply if you know anything about it.double thanks to repliers.

I post it here bcz i thought there are some persons whichc will think on it. I think none of you think.Howeveri think a bit and want to share it with you.
explanation for
1(a) let us assume that there is different current in upward upper and lower part of circuit. Now just reverse the direction of the circuit i mean upper part in lower and lower in upper. So the current slowing in upper part will now the current in lower part and current flowing in lower part willl in upper part. BUT the circuit is same as it was before reversing. So here arise contradiction which can killed if and only current in upper and lower region will same.
1(b) still now i have no idea for this.
2(a) It is much similar to 1(a) but in this case we require to revert the direction of current. If we take current different then contradiction will arise which can be cured only by taking current similar.
2(b) It is derivative of 2(a)
2(c) doesn't get;
2(d) One more thing that i can't explain.

hey friends please help yar;Tell me something that how it can.

This is wheat stone bridge. It is not affected by R_{s}.But think this is not the way of explaining any thing. I mean 2*2=4 and2+2=4. It does not mean that * is same as +.
How you can explain all the phenomena by one example. It's particular case.