Education7 min read
Number Sequence Puzzles, Explained From the Rule Up
A catalogue of the rule types behind number sequence puzzles, a first-pass procedure that beats guessing, and the honest limit of every such puzzle.
Topic hub · 18 articles
Logic and Pattern Puzzles
A puzzle feels like inspiration and is usually procedure. Number sequences have a small number of underlying rules; matrix problems vary a small number of attributes; syllogisms fail in a small number of predictable ways. Once you know the catalogue, most items become a search through it rather than a wait for insight.
This matters because the alternative — staring until something clicks — does not scale and does not survive a time limit. A systematic first pass tells you within seconds whether a sequence is arithmetic, geometric, recursive, interleaved, or built on differences of differences, and that is most of the work.
These articles cover the construction of each puzzle type, the solving procedure that fits it, and the specific reasoning errors that make otherwise-capable people get them wrong.
Where to start
Work the difference table first
For numeric sequences, first and second differences identify most rules immediately. The sequences guide covers the full procedure.
Name the attributes
Matrix items vary things like shape, count, rotation, shading and position. Listing the attributes before looking for the rule prevents the common failure of spotting one rule and stopping.
Know the standard traps
Affirming the consequent, illicit conversion and base-rate neglect account for a large share of wrong answers on deduction items. The reasoning-error articles cover them individually.
Start here
Everything else in this hub
- Education5 min read
Analogy Questions: Mapping the Relationship, Not the Words
State the relationship as a full sentence before reading the options. Analogy relationship types, how distractors are built, and worked verbal and number items.
- Education5 min read
Arithmetic Sequences: Constant Difference, Explained
What a constant difference is, how the nth-term rule is derived rather than memorised, and why the sum of an arithmetic sequence is just pairing.
- Education6 min read
Six Reasoning Mistakes That Show Up in Puzzles
Valid but untrue, one rule assumed unique, a conditional read backwards. Six errors that wreck puzzle answers, each with a checkable example and a fix.
- Education6 min read
If-Then Reasoning and the Two Mistakes Everyone Makes
From 'if P then Q' only two inferences are valid. The four forms, why the invalid pair feels right, the contrapositive, and what 'only if' actually means.
- Education6 min read
Deductive Reasoning, With Examples You Can Check
A deductive argument promises its conclusion cannot be false if the premises are true. Validity, soundness, the counterexample test, and why belief interferes.
- Education5 min read
Fibonacci and Other Recursive Sequences
What makes a sequence recursive, how Fibonacci and Lucas numbers differ only in their seeds, and which golden ratio claims actually hold up.
- Education6 min read
Finding the Rule: Difference Tables and Second Differences
A mechanical method for finding the rule behind a number pattern when inspection fails, using difference tables, constant rows and degree counting.
- Education5 min read
Geometric Sequences: Constant Ratio, Explained
How to spot a constant ratio, why the nth-term rule uses an exponent, and what negative ratios and ratios below one do to a sequence.
- Education6 min read
Inductive Reasoning and the Leap It Always Takes
Inductive arguments make a conclusion probable, never certain. The four common shapes, what makes one strong, and a sequence that punishes early confidence.
- Education5 min read
Solving a Logic Grid Puzzle Step by Step
A worked method for grid logic puzzles: mark negatives first, propagate every positive across its row and column, and use counting when elimination stalls.
- Education6 min read
How a Three-by-Three Matrix Puzzle Is Built
Matrix reasoning items are built from a few named rules running across rows and down columns. How the attributes, the rules and the wrong options are chosen.
- Education6 min read
Missing Number Problems: Undoing an Equation
Which inverse operation solves a missing number problem depends on where the blank sits. Worked examples, the two shapes that trip people up, and a check.
- Education6 min read
Odd One Out Across Words, Numbers and Shapes
An odd one out puzzle asks for a dimension on which one item differs. Why several answers are often defensible, and how a setter removes the ambiguity.
- Education6 min read
When a Sequence Puzzle Has More Than One Right Answer
Why a finite list of numbers never forces a single continuation, the convention that makes sequence puzzles answerable anyway, and how to check yours.
- Education6 min read
Syllogisms: All, Some, None and What Follows
Categorical statements come in four forms. The square of opposition, a circle-drawing method that settles validity, and the invalid forms that feel right.
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Visual Pattern Puzzles and the Four Rules They Use
Figural pattern puzzles run on translation, rotation, reflection and glide reflection, plus a counted attribute. How to name what changes, and check it.
- Education6 min read
Working Backwards: Solving a Problem From Its Answer
Know where a process ended but not where it started? Invert each step and reverse the order. Worked chains, the order trap, and how to check a result.