6.4 Multi-Rule Elimination and Final Verification
Key Takeaways
- Complex official examples use several simultaneous rules, so each variable should be solved separately before recombination.
- A choice that satisfies only the most obvious rule is a distractor, not a near-correct answer.
- The selected fifth figure must make the Frame 4-to-5 transition consistent with all earlier transitions.
Why partial-rule choices are persuasive
A complex sequence might contain three real rules and one random feature. Answer choices can be designed so that one matches location but not shading, another matches count but not orientation, and only one matches every rule. The eye often stops at the first familiar feature. A disciplined solver keeps a checklist.
The official explanations model this process. One worked problem identifies majority shading alternation and movement of a uniquely shaded sector, then checks each option against both. Another tracks rotating locations while holding a center object gray. A sample explanation later identifies four simultaneous rules: movement of two occupied boxes, decreasing count, and alternating shading, while changing shape is declared irrelevant.
Solve-predict-eliminate-verify
1. Solve one variable
Start with the clearest repeated feature. Write its four states and predict the fifth. Good starting variables are object count, a single marker's location, or simple shading alternation.
2. Predict before choices
State the required fifth-frame state for that variable. Prediction prevents an attractive choice from rewriting the rule.
3. Eliminate violations
Remove every option that fails the confirmed requirement. Do not reconsider those options unless the rule itself is disproved by a given frame.
4. Solve the next variable
If multiple choices survive, audit another feature. Continue until one remains.
5. Verify globally
Insert the selected choice as Frame 5. Confirm that each rule makes the same kind of transition from Frame 4 to 5 as before. Also confirm that a supposedly random feature was not actually following a cycle.
Example: rotating counts and shading
Imagine three columns inside each frame. The object counts are:
- Frame 1: 2, 1, 3
- Frame 2: 3, 2, 1
- Frame 3: 1, 3, 2
- Frame 4: 2, 1, 3
The whole count pattern rotates one column to the right and repeats after three transitions. Frame 5 must be 3, 2, 1. If fill also alternates dark/light/dark/light, Frame 5 must be dark. The identity of the objects—stars, circles, or squares—may vary randomly.
An option with 3, 2, 1 but light fill is a partial-rule distractor. An option with 2, 3, 1 and dark fill mis-rotates the counts. Only a dark 3, 2, 1 arrangement survives.
Example: two movers that overlap
Suppose marker A advances two positions each frame and marker B advances one. In Frame 3 both occupy the same location. Do not conclude that one marker vanished. Continue each path independently to predict Frame 4 and Frame 5. The official guide includes a sample in which two shaded boxes temporarily occupy the same position; recognizing overlap is necessary to preserve both movement rules.
Example: relationship plus random values
Two stacked polygons change from frame to frame. The top polygon has 4, 6, 3, and 5 sides—no simple time sequence. The lower polygon has 5, 7, 4, and 6 sides. The stable relationship is that the lower polygon always has one more side than the upper. If an answer choice shows a top triangle, the bottom must be a square, regardless of the prior top counts.
At the same time, shading may alternate between top and bottom and the pair may shift position. Solve relationship, shading, and position separately.
When the first rule fails
If no simple pattern explains all four frames:
- Check whether two alternating subsequences exist: Frames 1 and 3 follow one rule, Frames 2 and 4 another.
- Check whether a set of values rotates among positions.
- Check for a constant relationship inside each frame instead of change over time.
- Check whether two elements move at different rates.
- Reclassify a striking feature as random and examine a quieter one.
Do not jump to 3-by-3 matrix operations. The target remains the fifth member of a sequence.
Choice verification table
For a difficult item, compare survivors directly:
| Choice | Location rule | Count rule | Shading rule | Orientation rule | Keep? |
|---|---|---|---|---|---|
| A | pass | pass | fail | pass | no |
| B | pass | fail | pass | pass | no |
| C | pass | pass | pass | pass | yes |
This mechanical check reduces visual overload and prevents "almost right" choices from winning.
Time control
Fourteen items in 32 minutes allow careful work, but not unlimited reinvention. If you have confirmed one or two rules and narrowed the options, use the best supported choice. The official guide says incorrect guesses receive no extra penalty. Save time for later sequences, then review within the section if time remains.
Final verbal proof
Before confirming, complete the sentence: "Choice C is correct because marker A moves two spaces, the count rotates right, shading alternates, and outline shape is random." If you cannot name why the final choice survives, perform one more audit. If the explanation refers to a matrix row or an undisclosed test convention, return to the official four-frame sequence.
A choice matches the sequence's moving marker but violates a confirmed shading alternation. How should it be treated?