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Number-theory puzzle — rules and where to play

NUMBER-THEORY PUZZLE · Divisibility / Modular / Diophantine

Play with divisibility, remainders and primes over the integers. Clean rules, hard because you must think mod.

Origin
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Difficulty
★★★★★ 3–5 / 5
Time
10–40 min
Grid
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Sites
1

Rules

  1. Problems stay in integers (or positives); ask existence, count or construct.
  2. Tools: divisibility, gcd, modular arithmetic, prime factorisation.
  3. Classics: light bulbs (squares), Josephus, congruences.
  4. A correct answer is usually an exact integer, a count, or an explicit construction — not an approximation.

How to start

Find the period from small cases

Many cycle under a small modulus; hand-compute the first terms.

Factorise

Divisibility and counting often break via exponents after factoring.

Recognise the classic

Squares, Josephus, congruence recur — match first.

Write the invariant

Name what stays fixed (parity, residue class, gcd) before inventing a formula.

Where players get stuck

  • Using real-number intuition on integer problems, ignoring floor/parity.
  • Skipping small cases and taking a formula the long way.
  • Treating a working example as a proof without checking the modulus boundary.

Play Number-theory puzzle

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About this page
  • Last updated 2026-09-22
  • Source Curated compilation of established puzzle rules and listed third-party play sites
  • Audience Players learning Number-theory puzzle rules or looking for online sites to play
  • Covers Rules summary, how to start, common pitfalls, and the dedicated play sites listed on this page
  • Does not cover Hosted puzzles, worked solutions, official contest rankings, third-party uptime or pricing guarantees
  • Not advice This page is puzzle reference content only. It does not constitute financial, legal, medical or other professional advice.
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