Identify the picture given in the options which, when put in place of the…

Concept: In a figure series a single fixed rule is applied to the same base figure at every step. When small markers sit on the outside of a closed boundary, that rule is normally a fixed rotation: every marker moves through the same number of resting places, in the same direction, at every step. On a rectangle a small circle can touch the outside of the boundary at eight such resting places, which in clockwise order are: the top edge at its left corner, the top edge at its right corner, the right edge at its top corner, the right edge at its bottom corner, the bottom edge at its right corner, the bottom edge at its left corner, the left edge at its bottom corner, and the left edge at its top corner; after the eighth the cycle returns to the first.

Application: Read off, panel by panel, the resting place of each of the two circles in the given series.

Between one panel and the next, each circle advances exactly one resting place clockwise, so the pair always occupies two consecutive resting places and never separates.

Cross-check: Advancing the pair one more resting place from the fourth panel puts the first circle at the bottom edge, right corner and the second circle at the bottom edge, left corner.

An independent check agrees: the pair began along the top edge occupying both of its corners, and four clockwise moves cover four of the eight resting places, that is half the cycle, so the pair must again lie along a single edge occupying both of its corners, namely the bottom edge.

Contrast with the other arrangements:

• An arrangement with one circle outside the right edge at its top corner and one under the bottom edge at its right corner leaves a resting place empty between the two markers, so the pair is no longer consecutive.

• An arrangement with both circles under the bottom edge, one at its left corner and one part-way along the edge, places a marker between two corners instead of at a resting place.

• An arrangement with one circle under the bottom edge at its left corner and one outside the left edge at its bottom corner is the pair after one further clockwise move, that is the panel that would follow the missing one.

Answer: the picture in which two circles rest under the bottom edge of the rectangle, one touching that edge at its left corner and the other touching it at its right corner.