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  • Caesar Cipher
  • What it is
  • Key facts you need
  • Step-by-step solving workflow
  • Worked example (full walk-through)
  • Practice
  • Answers
  • Common mistakes
  • Quick reference
  • See also

Codebusters - Caesar

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Type: Inquiry
Divisions: B, C
Participants: Up to 3
Approx. Time: 50 minutes
Allowed Resources: Writing utensils; up to three Class I or Class II calculators. No external notes. Supervisor provides scratch paper and reference sheet.

Caesar Cipher

What it is

  • Every letter is shifted the same number of places through A–Z with wrap-around. Spaces and punctuation stay the same.
  • Example (k=3 forward): A→D, B→E, C→F; decode reverses the shift by k.
  • Hand rule for decode: rotate each letter backward by k; A backward 1 becomes Z, B backward 2 becomes Z, etc.

Key facts you need

  • Only 25 nontrivial shifts; you can try them all quickly.
  • Keep spaces/punctuation as-is; only rotate letters A–Z.
  • Clues: English has common short words (THE, AND, OF, TO) and E/T/A/O/N frequent; doubles like LL, EE, OO help confirm.

Step-by-step solving workflow

  1. Look for single-letter words. If you see X, test shifts that map X→A and X→I first.
  2. Try candidate shifts on 1–2 short words to see if they become English.
  3. Once a shift produces real words, apply it to the whole text and sanity-check the sentence.

Worked example (full walk-through)

Ciphertext

P EXTRT DU XPEEXCTHH HWDJAS CTKTG QT IPZTC PH SJT.

  1. Single-letter word P → test k=15 (P→A) or k=17 (P→I). Start with k=15.

  2. Test a few words with k=15 (shift letters 15 backward)

  • IPZTC → I→T, P→A, Z→K, T→E, C→N → "TAKEN"
  • PH → P→A, H→S → "AS"
  • Looks promising; keep k=15.
  1. Apply k=15 to all letters
A PIECE OF HAPPINESS SHOULD NEVER BE TAKEN AS DUE.

Everything is clean English; k=15 is correct.

Practice

  1. Decrypt with k=7 backward: ZOLSSZ
  2. Try mapping the single-letter word V to A first; decode: V DVYYL
  3. Try all shifts quickly for: URYYB JBEYQ (hint: standard ROT)

Answers

  1. SCHOOL
  2. With k=21 (V→A): I HELLO (short sample can be ambiguous; use more context in real problems)
  3. With k=13 (ROT13): HELLO WORLD

Common mistakes

  • Forgetting wrap-around (A backward 1 becomes Z).
  • Changing spaces/punctuation; only rotate letters.
  • Not testing A/I for single-letter words early.

Quick reference

  • Try single-letter words → A or I → test those shifts first.
  • If unclear, scan for THE/AND/OF, or run through all 25 shifts.
  • Keep non-letters unchanged; apply one global shift.

See also

  • Affine (generalizes Caesar), Atbash (a specific mirror mapping), Random Aristocrat (variable mapping).