Select the figure among the given options that can replace the question mark…
2023
Select the figure among the given options that can replace the question mark (?) in the following series.
Attempted by 6 students.
Show answer & explanation
Concept: A progressive figure series is generated by applying one and the same transformation to each figure in turn. The reliable method is to split a figure into its independently varying attributes — how many elements it contains, what kind each element is, and where each element sits — then track every attribute separately across the given figures, extend each attribute by exactly one further step, and accept only the figure that satisfies all of the extended attributes simultaneously. An attribute that never changes across the given figures is itself part of the rule and must be preserved in the answer.
Application: Every figure in this series is a stack of horizontal lines drawn one above another, in which exactly one line is thick and solid black and the rest are thin. Recording the attributes of the four given figures from left to right:
Figure in the series | Where the thick black line sits | Thin lines below it | Total lines |
|---|---|---|---|
First | Top of the stack | 1 | 2 |
Second | Top of the stack | 2 | 3 |
Third | Top of the stack | 3 | 4 |
Fourth | Top of the stack | 4 | 5 |
Fifth (to be found) | Top of the stack | 5 | 6 |
Extending each attribute by one step:
Position: the single thick black line is the topmost member of the stack in all four given figures. This attribute never changes, so it must stay topmost in the fifth figure as well.
Count of thin lines: the thin lines drawn below the thick line number 1, then 2, then 3, then 4 — one extra thin line is added at each step. One more step gives 5 thin lines.
Total lines: the totals run 2, 3, 4, 5, increasing by one each time, so the fifth figure holds 6 lines in all — consistent with 1 thick line plus 5 thin lines.
So the figure that replaces the question mark is the one showing a single thick black line at the top of the stack with five evenly spaced thin lines drawn below it, six horizontal lines in all.
Cross-check: testing the other available figures against the same two attributes:
A figure of five thin lines with no thick black line anywhere breaks the position attribute: the thick line is present in every given figure and is never dropped from the stack.
A figure of three lines whose thick black line lies lowest, with two thin lines above it, breaks both attributes: the thick line is no longer topmost, and no thin line lies below it instead of five.
A figure of four lines whose thick black line lies third from the top, with one thin line beneath it, also breaks both attributes: the thick line is not topmost, and only one thin line lies below it instead of five.
Reading the rule backwards confirms the same result: take the last of the given figures (thick line on top, four thin lines below, five lines in all), add one more thin line at the bottom of the stack and keep the thick line on top, and a six-line figure with five thin lines below the thick line is exactly what is produced.