Coding–decoding for AFCAT: letter shifts, opposites, reversals and word codes

In a coding–decoding question, a word is turned into a code by a hidden rule. You are shown one example, such as "FLY is written as GMZ", and asked to code or decode another word with the same rule.

The rules come from a short list, and one habit finds almost all of them: write the word and its code in two rows, one letter above the other, and compare each pair. Once you know the letter positions by heart, most coding questions take 30 to 45 seconds.

The tools: letter positions and opposites

• Positions: A = 1, B = 2, … Z = 26. The anchors E = 5, J = 10, O = 15, T = 20 and Y = 25 get you to any letter in one or two steps.
• Opposite letters: pairs whose positions add up to 27. A and Z, B and Y, C and X, and so on, ending with M and N. To find the opposite of any letter, subtract its position from 27.
• Wrap-around: after Z comes A again. So Y + 3 = B, and B − 3 = Y.

Write the alphabet with numbers on your rough sheet at the start of the reasoning section. It takes 20 seconds and saves far more.

The method

1. Write the word in one row and the code under it, letter by letter.
2. Compare each pair. Is the code letter a few places ahead or behind? Is it the opposite letter? Is it the same letter in a different place?
3. Look for the pattern in the shifts: the same every time, growing (+1, +2, +3), alternating (+1, −1) or position-based.
4. Check whether the order has changed. If the code uses the same letters rearranged, the word may be reversed or its halves swapped.
5. Apply the rule to the new word, and check one letter back against the example.

Why it works: a code is just a function applied to each letter, or to the order of letters. Writing word and code in rows turns the hidden function into a visible list of shifts that you can read directly.

The main code types

Worked examples

Example 1 (constant shift). If FLY is coded GMZ, how is AIR coded?

• F → G, L → M, Y → Z. Each letter moves +1.
• A → B, I → J, R → S: BJS.

Example 2 (opposite letters). If CAT is coded XZG, how is DOG coded?

• C (3) → X (24), A (1) → Z (26), T (20) → G (7). Each pair adds up to 27.
• D (4) → W (23), O (15) → L (12), G (7) → T (20): WLT.

Example 3 (growing shift). If MAP is coded NCS, how is JET coded?

• M → N is +1, A → C is +2, P → S is +3.
• J + 1 = K, E + 2 = G, T + 3 = W: KGW.

Example 4 (reverse and shift). If WING is coded HOJX, how is TAIL coded?

• The code letters H, O, J, X are one place after G, N, I, W, which is WING backwards. So the rule is: reverse the word, then shift each letter +1.
• TAIL reversed is LIAT. Shift +1: MJBU.

Example 5 (number value). If SKY = 55, what is FLY?

• S (19) + K (11) + Y (25) = 55, so the code is the sum of letter positions.
• F (6) + L (12) + Y (25) = 43.

Example 6 (word codes). In a code language, "sky is blue" is written "ta ro pi", "blue is calm" is "pi ro ka", and "calm sky above" is "ka ta mu". What is the code for "sky"?

• "Sky" appears in the first and third sentences. The only code word in both is "ta". So sky = ta.
• In the same way, "calm" (second and third sentences) = ka, and "above" = mu.
• Note what cannot be found: "is" and "blue" both appear in the first two sentences, which share "ro" and "pi". There is no way to tell which is which, so the code for "is" cannot be determined.

Decoding: running the rule backwards

Some questions give a code and ask for the word. Reverse every step of the rule, in reverse order.

• If the rule is "shift +2", decoding is "shift −2".
• If the rule is "reverse, then shift +1", decoding is "shift −1, then reverse".
• Opposite letters and reversal undo themselves: applying them twice returns the original word.

For example, if each letter is written as the letter two places before it, the code UGLE decodes by moving each letter forward two places: U → W, G → I, L → N, E → G, giving WING.

Practice set

1. If each letter moves one place forward, how is PLANE coded?
2. Code ARMY using opposite letters.
3. If ROAD is coded DAOR, how is BASE coded?
4. If JUMP is coded KWPT, how is BIRD coded?
5. If FLIGHT is coded GKJFIS, how is RADAR coded?
6. In a code language, "jets fly high" is "ka po ri", "high and low" is "ri su ve", and "fly low today" is "ve po zi". What is the code for "jets"?
7. If SKY = 55, what is AIR?
8. In a code, each letter is written as the letter two places before it. Decode YPKW.

Answers:

1. QMBOF. P → Q, L → M, A → B, N → O, E → F.
2. ZINB. A (1) → Z (26), R (18) → I (9), M (13) → N (14), Y (25) → B (2).
3. ESAB. The word is reversed.
4. CKUH. The shifts are +1, +2, +3, +4 (J → K, U → W, M → P, P → T). So B → C, I → K, R → U, D → H.
5. SZEZS. The shifts alternate +1, −1 (F → G, L → K, and so on). R + 1 = S, A − 1 = Z (wrapping round), D + 1 = E, A − 1 = Z, R + 1 = S.
6. ka. "Fly" is in the first and third sentences, which share only "po", so fly = po. "High" is in the first two, which share only "ri", so high = ri. That leaves "ka" for "jets".
7. 28. A (1) + I (9) + R (18).
8. ARMY. Move each letter two places forward: Y → A (wrapping round past Z), P → R, K → M, W → Y.

What to do next

• Learn positions and opposites until you can give either for any letter in two seconds.
• Solve 20 coding questions a day for a week, always writing word and code in two rows first.
• Practise number and letter series, which uses the same letter arithmetic, then try blood relations, where coded symbols stand for family relations.