In the figure above, three wires are braided. That is, by starting in the order A, B, C, the outer left wire A is brought over wire B to the middle position, forming the order shown in step 1, then the outer right wire C is brought to the new middle position shown in step 2, and so on, alternately bringing each new left and each new right wire to the middle. At what numbered step does the braid first repeat the original order A, B, C ?

(A) 3

(B) 4

(C) 5

(D) 6

(E) 7

Level of Difficulty E

This is a problem that involves mental manipulation of the given diagram, but it can be made much easier simply by tracking changes on paper as you go through the braiding process.

Step 1 BAC

Step 2 BCA

Step 3 CBA

Step 4 CAB

Step 5 ACB

Step 6 ABC

At Step 6 we return to the original positions of ABC, and that is choice D.

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