Number Challenges blog

Number theory, sequences, and reasoning guides. Start with numerical reasoning tests and number theory puzzles. Prefer to just solve? Jump in below.

• The Fibonacci Sequence Explained (and the Golden Ratio)

  The Fibonacci sequence explained: what it is, the simple rule behind it, its link to the golden ratio, where it appears in nature, and how it shows up in number puzzles.

• Prime Numbers Explained: What They Are and How to Find Them

  Prime numbers explained simply: what a prime number is, why 1 isn't prime, how to test if a number is prime, the Sieve of Eratosthenes, and where primes are used.

• Numerical Reasoning Tests: How to Solve Number Sequence Questions

  How to solve number sequence questions on numerical reasoning and aptitude tests. The checks that crack most series, worked examples, and timing tips for test day.

• Divisibility Rules: How to Tell What Divides a Number

  Divisibility rules for 2 to 12 with examples. Quick tests to tell whether a number is divisible by 3, 4, 7, 8, 9, 11 and more, and why they help solve number puzzles.

• Magic Squares: How They Work and How to Solve One

  Magic squares explained: what they are, the magic constant formula, a worked 3x3 example, the Siamese method for building odd squares, and how to solve a partial one.

• What Is Modular Arithmetic? Clock Math Made Simple

  Modular arithmetic explained simply as clock math. What 'mod' means, how the modulo operation works with examples, congruence notation, and where it's used.

• The Collatz Conjecture: The 3n+1 Problem No One Can Solve

  The Collatz conjecture explained: the simple 3n+1 rule, why the 'hailstone' numbers always seem to reach 1, worked examples, and why this easy-looking problem is unsolved.

• What Are Number Theory Puzzles? Types and How to Solve Them

  What number theory puzzles are and how to solve them. Divisibility, prime, remainder, and digit puzzles explained, with a constraint-and-elimination solving method.