Each puzzle is generated from the rule taxonomy identified in Carpenter, Just & Shell's (1990, Psychological Review) item-by-item analysis of the real Advanced Progressive Matrices: constancy, quantitative pairwise progression (size, count, orientation), distribution of three values (Latin square), figure addition/subtraction (OR/XOR), and — in the very hardest items — distribution of two values. Rules are applied consistently across the rows and columns of a 3×3 matrix, and difficulty scales the way it does in the real test: by stacking more, and harder, rules at once, plus close single-attribute-wrong distractors. The answer set is composed, not sampled: every active rule — including the marker overlay on the top tiers — gets at least one distractor that is wrong in that attribute alone, and rotation-wrong options are capped, so no single attribute (rotation especially) can ever be checked in isolation to find the answer.
Orientation rules follow the real test's convention: they are carried by asymmetric, direction-bearing elements (arrows, sectors, half-discs, bars) turned in clean 45°/90°/135° steps — never by near-symmetric polygons, where a turn can be visually ambiguous. Regular shapes appear only in puzzles where orientation is not one of the active rules.
Practicing this exact task reliably improves your score on it — you're learning the rule vocabulary and pattern language, which is exactly what a real test measures. It does not reliably raise general fluid intelligence itself: the research on cognitive training (e.g. working-memory training studies) generally shows strong near-transfer to the trained task and little far-transfer beyond it. Worth doing if your goal is the test; don't expect it to make you smarter in some broader sense.
The difficulty labels (e.g. "IQ 130+") are a rough heuristic — an approximate fluid-reasoning range for someone who solves that tier's items consistently — not a calibrated score from a normed, standardized administration. The top tier is capped at 130 because that's both Mensa's actual admission cutoff (98th percentile on a standard, SD-15 scale — not the sometimes-quoted 148, which is the same percentile on the differently-scaled Cattell test) and roughly where the real Raven's Advanced Progressive Matrices ceilings out: even a perfect raw score there only converts to about IQ 132–135 in the published norms, since the test wasn't built with enough super-hard items to discriminate further up. Treat these labels as a difficulty guide, not a real IQ measurement.
The Extreme tier sits above that ceiling on purpose and is deliberately unlabeled with any IQ number. It reuses the same rule taxonomy as the Mensa tier — all five fields active plus marker overlays — but stacks two independent overlay rules at once (e.g. one pair of marker positions following figure addition/subtraction while another pair follows distribution-of-two). That combination doesn't occur in the real Advanced Progressive Matrices item pool, so there's no published norm to map a score on it to an IQ figure — it's harder than real APM gets, not a higher-IQ estimate.
Extreme's answer options are also attribute-balanced, in the style of the I-RAVEN dataset (Hu et al., AAAI 2021) — a fix invented after machine-learning models were shown to solve Raven-like items from the answer options alone, without looking at the matrix. Three attributes (always including the markers) each take a wrong value in exactly half of the eight options, so the correct value of every attribute is never in the majority. Test-wiseness strategies — pick the most common value per attribute, response elimination — get zero statistical signal here. The real APM does not do this (its published distractor sets remain partly vulnerable to such strategies), which is another reason this tier sits outside the normed test.