VIC Selective Entry cheat sheet

Working backwards: if a result is given, reverse each operation in reverse order (add becomes subtract, multiply becomes divide).

Invariant principle: identify a quantity unchanged by every allowed move; if start and goal differ on it, the task is impossible.

Pigeonhole principle: placing n+1 items into n boxes forces at least one box to hold 2 or more items.

Parity check: a move that changes a total by an even number preserves its odd/even status; use parity to prove impossibility.

Extremal principle: examine the largest or smallest case first; it often forces the structure of any solution.

Symmetry shortcut: when a problem is symmetric between two options, any optimal answer treats them equally unless a constraint breaks the symmetry.

Rate equation: work done = rate x time; combined rate of workers acting together is the sum of their individual rates.

Check by substitution: after solving, substitute the answer into the original conditions, not just the final equation.

Valid argument test: an argument is valid only if no case makes all premises true and the conclusion false; validity is about form, not truth of premises.

Contrapositive equivalence: 'if P then Q' is logically identical to 'if not Q then not P'; the converse ('if Q then P') is not equivalent.

Necessary vs sufficient: P is sufficient for Q when P guarantees Q; P is necessary for Q when Q cannot occur without P.

Syllogism chain: 'all A are B' plus 'all B are C' yields 'all A are C'; chaining only works in the direction stated.

Quantifier negation: 'not all A are B' means 'at least one A is not B'; 'no A is B' negates 'some A is B'.

Analogy rule: map the relation, not the content - identify the precise link (part-to-whole, cause-to-effect, degree) before choosing a pair.

Sequence rule search: test differences, then ratios, then alternating or paired positions, then squares/cubes before assuming a random pattern.

Confirmation bias guard: a rule is only supported when a test could have failed; seek the case that would disprove the hypothesis.

Divergent-then-convergent cycle: generate many options without judging, then screen against fixed criteria such as feasibility, cost, and time.

SCAMPER prompts: Substitute, Combine, Adapt, Modify, Put to another use, Eliminate, Reverse - each generates a distinct transformation.

Constraint as fuel: adding an artificial limit (fewer parts, lower budget) forces novel combinations rather than incremental tweaks.

Remote association: ideas far apart in category combine into more original products than ideas already closely related.

Deferred judgement: evaluating during generation reduces the number of ideas produced; separation of phases increases output.

Analogy transfer: borrow a solution structure from an unrelated field (nature, sport, architecture) and test whether the mapping holds.

Inversion technique: ask how to guarantee failure, then design against each listed cause to reveal overlooked solutions.

Originality check: an idea counts as creative only if it is both novel relative to the brief and actually workable.

Main-idea test: the correct main idea must cover the whole passage; a detail true of one sentence is too narrow.

Inference limit: a valid inference must be forced by the text; a plausible real-world fact not stated is not an inference.

Tone words signal attitude: concessive markers ('admittedly', 'although') flag a qualification the author still rejects or limits.

Scope words matter: 'all', 'most', 'some', 'none' change truth conditions; match the passage's quantifier exactly.

Cause vs correlation: the text supports causation only when it states a mechanism or controlled comparison, not mere co-occurrence.

Pronoun tracking: resolve 'it', 'this', 'they' to the nearest grammatically consistent noun phrase before judging a claim.

Author vs quoted view: distinguish the writer's own position from views reported and criticised within the passage.

Evidence hierarchy: explicit statement outranks strong implication, which outranks weak suggestion; choose the strongest supported option.

Transfer check: name the underlying principle (e.g., supply and demand, feedback loop, natural selection), then confirm the new situation contains its conditions.

Scale reasoning: linear scaling multiplies length; area scales as the square and volume as the cube, so doubling size quadruples surface area.

Feedback loops: negative feedback stabilises a system toward a set point; positive feedback amplifies deviation away from it.

Opportunity cost: the true cost of a choice is the value of the best alternative forgone, not the money spent.

Margin vs total: decisions change at the margin - compare the extra benefit of one more unit with its extra cost.

Sample bias: a conclusion drawn from a self-selected or unrepresentative group does not transfer to the wider population.

Control comparison: to attribute an effect to a cause, hold all other variables constant and vary only the suspected factor.

Model limits: every model omits variables; check whether the omitted factor is negligible in the specific situation before applying it.