Select the figure that should come next in the series.

2020

Select the figure that should come next in the series.

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Attempted by 2 students.

Show answer & explanation

Concept

A figure-series puzzle is solved by tracking EACH element through the frames as an independent, rule-governed motion. Isolate every symbol, note where it sits in each frame (top, bottom, left, right), read off its repeating rule, and the answer is the single frame that continues every element's rule at once.

Application

Two elements move through the three given frames: a small diamond and a plus sign. Track each one separately.

  1. The diamond travels around the box anticlockwise: it sits at the left edge in frame 1, drops to the bottom in frame 2, then rises to the right edge in frame 3. Left, then bottom, then right continues anticlockwise to the top as the fourth stop.

  2. The plus sign alternates between the bottom and the top: bottom in frame 1, top in frame 2, bottom in frame 3. The next term of the bottom-top-bottom pattern is the top.

For frame 4 both rules agree: the diamond completes its loop at the top and the plus returns to the top. The missing figure is therefore the one showing the plus and the diamond resting together along the top of the box.

Cross-check

Check the period of each motion. The plus has period 2 (bottom, top, bottom, top); frame 4 is the fourth term, which must read top. The diamond's four-stop anticlockwise loop (left, bottom, right, top) likewise places it at the top on the fourth frame. Two independent checks agree, confirming the plus-and-diamond-at-top figure as the unique continuation.

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