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Free guide · Abstract reasoning · 5 min read

How to solve operator pipeline puzzles

Operator pipelines: induce, then execute

Worked examples define what each mystery operator does. Pin each one down from the examples first — then the question is pure bookkeeping.

Updated

A figure enters a chain of labeled boxes and comes out transformed; worked examples pin down what each box does, and then a question is asked. It isn't always 'run the chain forward': you may be given the OUTPUT and asked which input produced it, asked which single box explains a before/after pair, asked which box did nothing on this particular input, or asked which ORDER of three boxes reaches a target. Nothing here tests imagination — the examples fully determine every box. Solvers fail by half-reading the examples and 'sensing' the operators instead of proving them.

Induce one operator at a time

Compare a pipeline's input and output where only one box sits between them, or where you already know every other box. Ask: what single change explains this step — a rotation? a shading advance? added or removed elements? a size step? Write the box's meaning down (mentally or on scratch paper) the moment it's proven.

Demand two confirmations

One example can fit several stories — after 90° clockwise on a symmetric figure, 'rotate' and 'mirror' look identical. An operator is known only when it explains every appearance it makes across all examples. If two readings survive, find the example that separates them; well-built items always contain one.

Four ways the question flips

Backwards: given the output, undo the chain from the LAST box to the first, inverting each step (rotate 90° clockwise becomes 90° counter-clockwise). Idle box: a box that SETS a value ('make it solid') does nothing when the input already holds it — spot that box instead of forcing every box to 'do something'. Which box?: one before/after pair, one change — name the single box that explains it. Which order?: three boxes used once each, where one RESETS a channel another one steps — only what follows the reset survives, so order is everything.

The strategy

  1. Read the examples before the question — they are the definitions.
  2. Decode boxes in order of exposure: the box you can see acting alone first.
  3. Confirm each decoded box against its other appearances.
  4. Execute the query chain one box at a time, updating the figure fully before the next box.
  5. Predict the final figure, then find it among the options.

Common traps

  • Treating a back-solve like a forward run — those items reverse the pipeline on purpose: last box first, each step inverted.
  • An operator induced from one example that breaks on the second (the planted ambiguity).
  • Carrying a half-updated figure into the next box — apply each operator completely.
  • Options showing the result of skipping exactly one box: if your answer isn't there, re-run the chain.

Speed · ~60s/item: Decoding is the investment; execution is fast. Spend up to half your time proving the operators — a proven pipeline runs itself.

Worked example

Made by the same generator and answer checker as the practice questions, at middling difficulty, but never served in a test. Commit to an option before you reveal — the pick is yours alone and is never recorded.

Each box always applies the same hidden rule, shown by its worked examples. What comes out of the pipeline?

▲ ■
?
Reveal the answer

The answer is D.

Show why — the worked reasoning
Induce each box's rule from its two worked examples — a rule must explain BOTH examples, not just one. Here box ▲ clears every dot from the top; box ■ grows the figure one size step (wrapping large → small). Now look at the input before you start transforming: it is already free of dots, so box ▲ has nothing left to do and passes the figure through untouched. A box whose rule names a target value only changes figures that miss that target. Apply the other boxes in order and leave the rest of the attributes alone. The tempting wrong answer is the one that lets box ▲ move the dot count anyway.

Try it yourself: 4 practice questions

Pick an answer, then reveal it. Nothing is recorded, there is no clock, and none of these questions is ever used in a test.

Question 1 · Easy

Each box always applies the same hidden rule, shown by its worked examples. Which single box turns the left figure into the right one?

?
Reveal the answer

The answer is C — ■.

Show why — the worked reasoning
Work backwards from the pair instead of forwards from a rule. First read what changed between the two figures — here the dot count, and nothing else. Then check which box's rule produces exactly that change: box ▲ makes the figure solid, whatever shading it arrived with; box ■ clears every dot from the top; box ● swaps outlined shading for hatched and back again (a solid figure is left as it is); box ◆ swaps the shape for the next one in the cycle (circle → square → triangle → circle). Only box ■ does it. No other box writes the dot count at all, so every other box is ruled out by an attribute that did NOT change. Any box that writes an attribute the pair leaves untouched is ruled out immediately.
Question 2 · Easy

Each box always applies the same hidden rule, shown by its worked examples. Which single box turns the left figure into the right one?

?
Reveal the answer

The answer is A — ◆.

Show why — the worked reasoning
Work backwards from the pair instead of forwards from a rule. First read what changed between the two figures — here the size, and nothing else. Then check which box's rule produces exactly that change: box ▲ makes the figure solid, whatever shading it arrived with; box ■ turns the figure back upright, whichever way it arrived; box ● rotates the figure 90° clockwise; box ◆ makes the figure the largest size, whatever size it arrived at. Only box ◆ does it. No other box writes the size at all, so every other box is ruled out by an attribute that did NOT change. Any box that writes an attribute the pair leaves untouched is ruled out immediately.
Question 3 · Easy

Each box always applies the same hidden rule, shown by its worked examples. What comes out of the pipeline?

▲
?
Reveal the answer

The answer is A.

Show why — the worked reasoning
Induce each box's rule from its two worked examples — a rule must explain BOTH examples, not just one. Here box ▲ rotates the figure 90° clockwise. Then push the new input through the boxes in order, transforming one attribute at a time. The wrong options each skip exactly one box or apply the last box twice — check every attribute against your predicted result.
Question 4 · Easy

Each box always applies the same hidden rule, shown by its worked examples. What comes out of the pipeline?

▲
?
Reveal the answer

The answer is D.

Show why — the worked reasoning
Induce each box's rule from its two worked examples — a rule must explain BOTH examples, not just one. Here box ▲ swaps outlined shading for hatched and back again (a solid figure is left as it is). Then push the new input through the boxes in order, transforming one attribute at a time. The wrong options each skip exactly one box or apply the last box twice — check every attribute against your predicted result.

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