How to find the equivalent resistance of this electric circuit?

[Leonid92]

Summary: How to find equivalent resistance of the electric circuit?

I need to solve the following problem:
Calculate equivalent resistance of the circuit (figure1), if all six resistances are the same: r1 = r2 = r3 = r4 = r5 = r6 = 100 Ohm.
True answer: 66.6 Ohm.

I tried to solve this problem, but I obtained wrong answer. Initially, I suppose that current will not flow to r5 and r6, since there is a wire without any resistor, and therefore the current will flow to where there is no resistance. Thus I consider that r5 and r6 are absent (see figure2 and figure3). After that, equivalent scheme looks like in figure4.
r1 and r2 are connected in parallel, and r3 and r4 are connected in parallel. Total resistance:
r = r12 + r34 = (r1*r2)/(r1+r2) + (r3*r4)/(r3+r4) = (100*100)/(100+100) + (100*100)/(100+100) = 100 Ohm.
Could you please write, how should I calculate equivalent resistance of given circuit?

 

[lewando]

You are correct to assert that R4 and R5 (<-- look! a typo! EDIT: I meant R5, R6) are superfluous. What makes you think that the "true answer" is 66.6 Ohms?

 

[Leonid92]

You are correct to assert that R4 and R5 are superfluous. What makes you think that the "true answer" is 66.6 Ohms?

The true answer is given in problems section for specific chapter of the electrical engineering textbook (The chapter is called "Simple DC electrical circuits"). It is old textbook published in 1989, and there are some mistakes in it, but I thought that the answer given in this book for the problem that I posted is unlikely to be wrong.

 

[lewando]

Mistakes in textbooks can be very frustrating. If you find 2 or 3, then soon everything is cast in doubt (as it probably should be). It forces you to do several things: trust your methods (which are hopefully correct), try alternate methods, look at other textbooks (or internet resources) for confirmation of a suspicion, and probably most importantly, develop a strong foundation in the subject matter.

By the way, I am operating in bufoon mode today. I was trying to edit post #2 to correct an irony-laden typo-- not R4, R5, but rather R5, R6. I killed the post instead. I suppose as humans, we are constrained by our humanity.

 

[Leonid92]

Mistakes in textbooks can be very frustrating. If you find 2 or 3, then soon everything is cast in doubt (as it probably should be). It forces you to do several things: trust your methods (which are hopefully correct), try alternate methods, look at other textbooks (or internet resources) for confirmation of a suspicion, and probably most importantly, develop a strong foundation in the subject matter.

By the way, I am operating in bufoon mode today. I was trying to edit post #2 to correct an irony-laden typo-- not R4, R5, but rather R5, R6. I killed the post instead. I suppose as humans, we are constrained by our humanity.

I understood that there was typo in post #2 :)
Thank you for your reply!

 

[NascentOxygen]

100 Ohm.

Your sequence of simplifications looks right.