Non-Verbal and Pattern Reasoning
Continue rotation patterns and apply mirror transformations to structured figure data.
What you'll learn
- Continue a constant-step rotation series, wrapping correctly past 360 degrees
- Apply a horizontal mirror transformation to a grid-based figure
- Distinguish rotation from mirroring as two different transformations
Prerequisites
Explanation
Non-verbal reasoning questions show a sequence of figures instead of words or numbers, and ask you to continue the pattern or identify a transformation. Since a figure can't be typed into a formula directly, the actual skill is describing the figure's properties as data -- angle, count, fill, orientation -- and then reasoning about how that data changes step to step, exactly the same way you'd reason about a number series.
A rotation series shows a shape rotating by a constant angle each step: 0 degrees, 90 degrees, 180 degrees, and so on. The same "find the constant step" method from number series applies directly, with one addition: angles wrap at 360 degrees. A step of 90 degrees from 300 degrees doesn't reach 390 degrees; it wraps to 30 degrees.
A mirror transformation flips a figure left-to-right (or top-to-bottom), reversing its horizontal (or vertical) orientation without rotating it. This is a completely different operation from rotation, and the two are easy to confuse: a shape rotated 180 degrees can look similar to its mirror image for symmetric shapes, but for an asymmetric shape (like a letter "F" or an arrow), rotation and mirroring produce visibly different results. Representing a row of a figure as an array (say, [1, 1, 0] for filled-filled-empty) makes a horizontal mirror concrete: reverse the array to get [0, 1, 1].
The general lesson: whenever a figure can't be typed directly, describe it with the smallest set of numbers that captures what's changing (an angle, a fill pattern, a count), and the reasoning collapses back to the same series and transformation logic you already know.
Example
Continuing a constant-step rotation series, wrapping past 360 degrees.
function nextInRotationSeries(degrees) {
const step = degrees[1] - degrees[0];
const next = (degrees[degrees.length - 1] + step) % 360;
return next < 0 ? next + 360 : next;
}
// nextInRotationSeries([300, 330]) -> 0 (wraps past 360)Guided exercise
Guided exercise
Write nextInRotationSeries(degrees), an array of angles with a constant step between them. Return the next angle, wrapping correctly if it would reach or exceed 360.
Checks: Continues a simple rotation series · Wraps correctly past 360 degrees · plus 1 hidden check
Code editor. Press Escape then Tab to leave the editor if keyboard focus becomes trapped. Press Control+Shift+M inside the editor to toggle Tab-key focus trapping.
Stuck? Get a hint.
Independent exercise
Independent exercise
Write mirrorGrid(grid), a 2D array of 0/1 values representing rows of a figure. Return a new grid where every row is reversed (a horizontal mirror), leaving the row order unchanged.
Checks: Mirrors a single-row figure · Mirrors a multi-row figure, row order preserved · plus 1 hidden check
Code editor. Press Escape then Tab to leave the editor if keyboard focus becomes trapped. Press Control+Shift+M inside the editor to toggle Tab-key focus trapping.
Stuck? Get a hint.
Common mistakes
- Confusing a mirror transformation with a 180-degree rotation -- they only look the same for symmetric figures.
- Forgetting that rotation angles wrap at 360 degrees.
- Trying to reason about a whole figure at once instead of breaking it into the specific properties (angle, fill, count) that are actually changing.
Knowledge check
Takeaway
Describe a figure with the smallest set of numbers that captures what's actually changing -- the reasoning then works exactly like a series or transformation you already know.
Summary
Non-verbal reasoning reduces to the same series and transformation logic used elsewhere, once a figure is described as data: rotation series follow a constant angular step (wrapping past 360), while mirroring reverses orientation without rotating.
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