Coding - Decoding
🔒 Log in to trackReversal and reverse-plus-shift coding
🔒 Log in to trackThe code is the word written backwards, possibly after shifting each letter. Test for it in one move: read the coded word backwards; if you see the sample word (or a uniform shift of it), the rule is reverse (+ shift k).
Skeleton: LOGIC → CIGOL (pure reversal). TABLE → FMCBU (reverse TABLE → ELBAT, then +1 per letter). Order matters: check 'reverse then shift' first, then 'shift then reverse' — both appear in CGL and they are not the same rule.
Detailed notes
What is reverse coding?
Hold a word in front of a mirror and you see it backwards. Reverse coding writes the word from right to left: LOGIC becomes CIGOL. Examiners like to add one more step, such as a shift after reversing, or they replace each letter by its opposite letter in the alphabet. All three ideas are covered in this lesson.
1. Pure reversal
Write the last letter first and the first letter last. GARDEN → NEDRAG. Test: read the code from right to left. If you get the original word, the rule is pure reversal.
2. Reverse and shift
The code is the reversed word with every letter moved by the same amount.
Example: PAINT → UOJBQ. Reverse PAINT → TNIAP. Compare TNIAP with UOJBQ: T→U, N→O, I→J, A→B, P→Q — each +1. So the rule is reverse, then +1.
When the shift is the same for every letter, 'reverse then shift' and 'shift then reverse' give the same result. When the shift changes by slot (+1, +2, +3 ...), the order matters, so copy the order used in the sample.
3. Opposite letters
Fold the alphabet in the middle: A sits on Z, B on Y, C on X, and so on. Each pair is called opposite letters. The positions of a pair always add up to 27.
| A-Z | B-Y | C-X | D-W | E-V | F-U | G-T |
|---|---|---|---|---|---|---|
| H-S | I-R | J-Q | K-P | L-O | M-N |
Memory aid: 'AZ', 'BY', 'CX' then 'DeW', 'EVe', 'FUn', 'GT', 'HS', 'IR', 'JQ', 'KP', 'LO', 'MN'. To find an opposite quickly: opposite = 27 − position. Example: opposite of K(11) = 27 − 11 = 16 = P.
How to spot it: take the first letter of the word and the first letter of the code. If their positions add to 27, check one more letter. Example: WHITE → DSRGV. W(23) + D(4) = 27, H(8) + S(19) = 27. Opposite letters confirmed.
4. Opposite and reverse together
Some codes first write the opposite letters and then reverse the whole word. LAMP → opposites OZNK → reversed KNZO. Test: if the first code letter is the opposite of the last word letter, both steps are present.
Decoding
- Reversal undoes itself: reverse the code to get the word.
- Opposite letters also undo themselves: the opposite of the opposite is the same letter.
- For reverse + shift, first un-shift, then reverse (or the other way; with a flat shift both orders work).
Common traps
- Reversing but forgetting the extra shift.
- Using 26 instead of 27 for opposites (26 − 11 = 15 = O is wrong; the opposite of K is P).
- In odd-length words the middle letter stays in the middle after reversal, but it still gets the shift or opposite.
Quick revision
- Read the code backwards first: word appears → reversal.
- Word appears shifted → reverse + shift; find k from one letter.
- Positions add to 27 → opposite letters; opposite = 27 − position.
- First code letter pairs with the last word letter → opposite + reverse.
- Reversal and opposite undo themselves when decoding.
Types of questions asked
Every way this subtopic shows up in exams — how to recognise it, the formula or logic to use, and a solved example.
Type 1: Pure reversalcommon2 practice Q
The code has the same letters as the word, written from right to left (GARDEN → NEDRAG).
- Read the code backwards; you should see the sample word.
- Write the new word backwards.
- For decoding, reverse the code.
Why it works: reversal is its own undo.
Example: If GARDEN is written as NEDRAG, how is FLOWER written?
Pure reversal → REWOLF.
Type 2: Reverse and then shiftcommon3 practice Q
Reading the code backwards gives the sample word with every letter moved by the same (or patterned) amount.
- Reverse the sample word.
- Compare the reversed word with the code letter by letter to find the shift.
- Reverse the new word and apply the same shift in the same order.
Why it works: two simple rules in a row.
Example: If PAINT is written as UOJBQ, how is BRUSH written?
PAINT reversed = TNIAP; TNIAP → UOJBQ is +1. BRUSH reversed = HSURB; +1 → ITVSC.
Type 3: Opposite letters (positions add to 27)common3 practice Q
Code letters look far from the word letters, and each word letter + its code letter = 27 (A↔Z, M↔N).
- Add the positions of the first word letter and first code letter; 27 means opposites.
- Confirm with one more letter.
- Write the opposite of each letter of the new word (27 − position).
Why it works: opposite pairs are fixed, so the code is a simple look-up.
Example: If WHITE is written as DSRGV, how is GREEN written?
W+D = 23+4 = 27 → opposites. GREEN: G↔T, R↔I, E↔V, E↔V, N↔M → TIVVM.
Type 4: Opposite letters plus reversaloccasional2 practice Q
The first code letter is the opposite of the LAST word letter; the code is the opposite word read backwards.
- Pair the first code letter with the last word letter (sum 27).
- For the new word, write the opposite letters, then reverse the result.
Why it works: both steps are self-undoing, so the order does not change the answer.
Example: If LAMP is written as KNZO, how is DESK written?
LAMP → opposites OZNK → reversed KNZO ✓. DESK → opposites WVHP → reversed PHVW.
Shortcut tricks
⚡ Backwards reading test
Read the code from right to left. If it equals the sample word, code new words by writing them backwards. If it is almost the sample with every letter off by the same k, code new words by reverse-then-shift.
Example: Q. If TABLE = FMCBU (reverse + 1), code CHAIR.
Sol. CHAIR reversed = RIAHC; shift +1 → SJBID.
One backwards read identifies the family; the shift value falls out of the first letter.
Where students lose marks
Reversing but forgetting the extra shift (or shifting before reversing when the sample did it the other way).
Reversing the probe but keeping the sample's letter order in the middle letters.
Applying reversal to decode questions without un-reversing the shift as well.
Practice sets — 12 questions
Sets of 10, mixed across the question types above. Each answer comes with a step-by-step explanation.
Topic test · 12 questions
Suggested time 8 min · wrong answers go to your mistake notebook automatically.