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**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?