How to Solve Pattern Completion (Figure Series)
Solve figure-series pattern completion questions by tracking rotation, shading and count independently, with worked examples.
Expected Interview Answer
A figure-series pattern completion question is solved by tracking each visual attribute — rotation, shading, size, element count — across the whole sequence independently to find its own per-step increment, then projecting every attribute forward to the next figure.
Instead of treating the series as one holistic pattern, break it into separate attribute tracks: does rotation increase by a constant angle each step, does shading cycle through a fixed set of states, does the element count increase arithmetically, or does size alternate? Each track is checked for either a constant additive step (rotate +30 degrees each figure) or a cyclic repeat (shading cycles white, grey, black, white, grey…), and the two behave differently when projecting forward. Once every attribute’s own rule is confirmed against all given figures in the sequence, the next figure is constructed by advancing each attribute independently by its own rule, not by assuming all attributes change in lockstep. The final check is to verify the constructed figure against the sequence’s starting point too, since some patterns are cyclic and loop back after a fixed number of steps.
- Independent attribute tracking catches patterns where different features change at different rates
- Explicitly checking for cyclic vs. additive rules avoids miscounting a repeating cycle
- Verifying against the sequence start catches cyclic patterns that would otherwise be missed
AI Mentor Explanation
A series of field-setting diagrams where the number of slip fielders increases by one each figure while the bowler’s run-up angle cycles through three fixed positions is solved by tracking the fielder count as an additive rule and the angle as a cyclic rule separately, not assuming both change the same way. Projecting the next figure means adding one more fielder while advancing the angle cycle to its next fixed position, which is exactly the independent-attribute-tracking discipline pattern completion tests.
Worked example
Attribute 1: dot count
- +2 each step (additive)
- Next: 9 dots
Attribute 2: shading
- Cycles white→grey→black (period 3)
- Next: white (cycle restarts)
Constructed figure
- 9 dots, white shading
Step-by-Step Explanation
Step 1
List independent attributes
Separate rotation, shading, size, and element count into their own tracks.
Step 2
Classify each rule
Determine if each attribute follows a constant additive step or a cyclic repeat.
Step 3
Verify against all figures
Confirm each attribute’s rule holds for every given figure in the sequence, not just the first two.
Step 4
Project forward independently
Advance each attribute by its own rule to construct the next figure, checking cyclic wrap-around.
What Interviewer Expects
- Separate tracking of each visual attribute rather than one holistic guess
- Correct classification of additive vs. cyclic rules per attribute
- Verification of each rule across the entire given sequence
- Correct handling of cyclic wrap-around when projecting the next figure
Common Mistakes
- Assuming all attributes change in lockstep with the same rule
- Miscounting a cyclic pattern’s period, leading to a wrong wrap-around figure
- Deriving a rule from only the first two figures instead of the full sequence
- Overlooking a periodic (every-nth-step) attribute that doesn’t appear in every figure
Best Answer (HR Friendly)
“I break the figure series into separate attributes — rotation, shading, size, count — and figure out each one’s own rule independently, because these series often mix a steady, additive change in one attribute with a repeating, cyclic change in another. Once I have confirmed each attribute’s rule against every figure given, not just the first two, I project each one forward on its own schedule to build the next figure, and I double check cyclic attributes for when they wrap back to their starting state.”
Follow-up Questions
- How do you distinguish an additive rule from a cyclic rule when only three figures are given?
- What is your approach when one attribute changes only every few figures rather than every figure?
- How would you handle a figure series with three or more independently changing attributes?
- How does pattern completion for figures differ from pattern completion for number series?
MCQ Practice
1. A figure series shows shading cycling white, grey, black, white, grey. What shading comes next?
The cycle has period 3 (white, grey, black); after white, grey the next in the repeating cycle is black.
2. A series shows dot count 2, 4, 6, 8 while rotation stays constant. What is the rule for dot count?
The count increases by exactly 2 each step, a constant additive rule, not a cyclic or multiplicative one.
3. Why is it risky to derive a figure series rule from only the first two figures?
Cyclic and additive rules can appear identical over just two steps; a third or later figure is needed to confirm whether the pattern repeats.
Flash Cards
What are the two main rule types for a figure-series attribute? — Constant additive step, or cyclic (repeating) pattern.
Why track attributes independently in a figure series? — Different attributes (rotation, shading, count) often follow different, unrelated rules.
What should you double-check for cyclic attributes? — The wrap-around point — when the cycle restarts from its first state.
Why verify a rule against the full sequence, not just two figures? — Two figures can look consistent with multiple rules; more figures disambiguate them.