Lessons / Logical reasoning
Logical reasoning · Day 9

Coding and Decoding

Find the rule from the one example, then test it on a second letter before you trust it. Most codes are a shift, a reversal, or a position-sum.

Practise (7 questions) Present as slides

Why this topic matters

If CAT is written as DBU, each letter moved one step forward. Coding questions hide a simple rule like that; your job is to find it and apply it.

Coding appears in almost every reasoning section. Most codes are one of four kinds: shift, reverse, opposite letter, or position number.

The four common codes

Shift: every letter moves the same number of steps (CAT → DBU is +1). The shift can also change per letter (+1, +2, +3 ...).

Reverse: the word is written backwards, sometimes with a shift too.

Opposite: each letter becomes its mirror in the alphabet (A <→ Z, B <→ Y). Pairs always add to 27.

Numbers: letters become their positions (CAT → 3 1 20), or the sum of positions.

A126B225C324D423E522F621G720H819I918J1017K1116L1215M1314N1413O1512P1611Q1710R189S198T207U216V225W234X243Y252Z261
Letter positions: A=1 ... Z=26 (reverse position underneath). Opposite pairs add to 27
Example 1If MOTHER is coded as NPUIFS, how is FATHER coded?
  1. M → N, O → P, T → U: each letter +1.Compare letter by letter.
  2. FATHER +1 = GBUIFS.
Example 2If GOLD is coded as TLOW, how is SILK coded?
  1. G (7) → T (20): 7 + 20 = 27. O → L: 15 + 12 = 27.Opposite letters add to 27.
  2. SILK → HROP.
Example 3If CAT = 24, what is DOG?
  1. C + A + T = 3 + 1 + 20 = 24.Sum of positions.
  2. D + O + G = 4 + 15 + 7 = 26.

Sentence codes ('Chinese' coding)

You get several sentences and their codes. Words common to two sentences share a common code. Compare sentences in pairs and cross out what matches.

Example 1'sky is blue' = 'ta na pa', 'blue is deep' = 'na ka ta', 'sky and sea' = 'pa ro mi'. What is the code for 'deep'?
  1. Sentences 1 and 2 share 'is' and 'blue', and codes 'ta' and 'na'.Common words match common codes.
  2. Sentence 2's remaining word 'deep' matches its remaining code.
  3. 'ka'.

Formula summary

Shift code
Each letter moves +k (or -k). CAT → DBU is +1.
Reverse alphabet
A <→ Z: position becomes 27 - position.
Number code
Letters to positions, sometimes summed or multiplied.
Word substitution
'Sky is called sea' → answer with the NEW name.
Chinese / sentence code
Compare two sentences: the common word and the common code match.

Shortcuts and tricks

Sentence code by overlap

Use it when: 'pit na sa' = you are good, 'na ho pit' = are you fine ...

  1. Words common to two sentences map to codes common to the same two sentences.
  2. Peel them off one at a time.
Example'la pe ro' = sweet hot coffee, 'ro ki ne' = coffee is good, 'pe ne ta' = hot good tea. Code for 'good'?
  1. 'coffee' is in sentences 1 and 2; the only code in both is 'ro'.
  2. 'good' is in 2 and 3; the only code in both is 'ne'.

Before you move on, you should be able to...

  • test shift, reverse, opposite and number codes in that order
  • use 27 to find opposite letters
  • match common words to common codes

Practice questions (7)

Try each one before opening the solution. Or practise them one by one so your score is saved.

easy If COMPUTER is coded DPNQVUFS, how is MOUSE coded?
  1. Each letter +1.

Answer: NPVTF

easy If CAT = 24 (sum of positions), DOG = ?
  1. 4 + 15 + 7.

Answer: 26

easy If MANGO is coded OCPIQ, how is APPLE coded?
  1. +2 each.

Answer: CRRNG

medium If GREEN is coded TIVVM (reverse alphabet), how is BLUE coded?
  1. B → Y, L → O, U → F, E → V.

Answer: YOFV

medium If 'water' is called 'air', 'air' is called 'fire', and 'fire' is called 'sky', what do fish live in?
  1. Fish live in water, and water is called 'air'.

Answer: air

medium If TEACHER is coded VGCEJGT, how is STUDENT coded?
  1. +2 each.

Answer: UVWFGPV

hard If FRIEND is coded HUMJTK, how is CANDLE coded?
  1. F+2, R+3, I+4, E+5, N+6, D+7.
  2. Apply the same shifts to CANDLE.

Answer: EDRIRL

Class plan (2 hours, for trainers)

A tested order for teaching this topic in one 2-hour session. Present mode follows the same order.

10 minWarm-up: letter positions with EJOTY.
30 minShift, reverse, opposite, numbers: one example each, then mixed.
20 minSentence codes.
15 minSubstitution codes ('sky is called water').
40 minPractice set.
5 minRecap.
← SeriesDirections →
Coding and DecodingPractise now