Study the diagram given below. Two fully worked chains show how the symbols…
2023
Study the diagram given below. Two fully worked chains show how the symbols (operators) between the figures transform one figure into the next. Using the same rules, select the option that will replace the question mark and complete the incomplete chain shown at the bottom.
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In a symbol-based figure analogy, each operator icon placed between two figures stands for one fixed visual transformation, such as adding a line, rotating a line, flipping a diagonal's direction, or inverting the background colour.
The meaning of each symbol has to be read off from the fully worked chains drawn in the diagram, and then applied in the same order to the new starting figure to find the missing figure.
Symbol | Effect on the figure |
|---|---|
⌘ | Adds an ascending diagonal (bottom-left to top-right) to the figure; any existing line and the background colour are left unchanged. |
H | Rotates the figure's straight line by 90 degrees: a horizontal line becomes vertical and a vertical line becomes horizontal; the diagonal and the background colour are left unchanged. |
X | Flips the diagonal's direction from ascending to descending (top-left to bottom-right), and inverts the background colour from black to white; the straight line is left unchanged. |
● | Leaves the figure unchanged; the fully worked top chain establishes this directly, since the figure drawn after the diagonal-adding symbol followed by this symbol is identical to what the diagonal-adding symbol alone would give. The fully worked chain branching from the top-right figure ends consistently with the same rule, though its intermediate state after the colour-and-diagonal symbol is not separately drawn. |
The incomplete chain's starting figure (shown at the bottom of the diagram) has a black background with a horizontal line and an ascending diagonal -- the same combination seen partway along the fully worked top chain, right after its diagonal-adding symbol.
Apply the line-rotation symbol (H): the horizontal line rotates to a vertical line, while the ascending diagonal and the black background stay unchanged. The figure now has a black background, a vertical line, and an ascending diagonal.
Apply the colour-and-diagonal symbol (X): the diagonal flips from ascending to descending, and the background inverts from black to white; the vertical line carries over unchanged. The figure now has a white background, a vertical line, and a descending diagonal.
This matches the independent worked chain on the right of the diagram: applying the same colour-and-diagonal-flip operator to a figure with a vertical line and an ascending diagonal on a black background also produces a white background with a descending diagonal, with the vertical line retained.
The option with a black background and an ascending diagonal already carries the vertical line produced by the line-rotation symbol, but neither part of the colour-and-diagonal symbol -- not the colour inversion, not the diagonal flip -- has been applied to it; it represents the figure exactly as it stood right after the line-rotation symbol alone.
The option with a black background and a descending diagonal shows the diagonal flip but not the colour inversion, so the colour-inversion half of the colour-and-diagonal symbol is missing.
The option with a white background and an ascending diagonal shows the colour inversion but not the diagonal flip, so the diagonal-flip half of the colour-and-diagonal symbol is missing.
The option with a white background, a descending diagonal, and the vertical line carried through unchanged is the only figure consistent with both the line-rotation symbol and the colour-and-diagonal symbol, and is therefore the correct completion of the pattern.