Coding-Decoding

Mental model

Every letter is a number in disguise.

Alphabet characters operate on a fixed mathematical ring (1 to 26). Visualizing them as numbers reveals the mathematical operations (+1, -2, reverse) hiding behind random letters.

Method

1. Write the alphabet and assign numerical positional values (A=1...Z=26). Keep reverse mappings (A=26...Z=1) handy.
2. Write the original word and its coded version stacked directly underneath each other. This visualizes vertical alignment.
3. Check for direct letter shifting. Calculate the numerical difference between the stacked letters (+1, -2, +3, etc.).
4. If vertical shifts don't make a pattern, check for cross-patterns (first letter codes to last letter) or halves-reversal (split word in half and reverse each).
5. Once the exact mathematical or positional rule is confirmed on the example, apply it strictly to the target word.

Worked example

Problem: In a certain code language, 'WATER' is coded as 'YCVGT'. How will 'FIRE' be coded?

1. Stack the words vertically: W -> Y, A -> C, T -> V, E -> G, R -> T.
2. Convert to numbers: W(23)->Y(25) is +2. A(1)->C(3) is +2. T(20)->V(22) is +2. E(5)->G(7) is +2. R(18)->T(20) is +2.
3. Identify the pattern: The rule is simply +2 to every letter.
4. Apply the rule to 'FIRE': F(6) + 2 = H(8). I(9) + 2 = K(11). R(18) + 2 = T(20). E(5) + 2 = G(7).
5. Combine the resulting letters: H, K, T, G.

Answer: HKTG

Common mistakes

• Ignoring wrap-around: Forgetting that adding to Z wraps around to A (e.g., Z + 2 = B) leads to calculation errors.
• Stopping after the first letter: Assuming the shift rule is constant (e.g., +1 everywhere) just because the first letter is +1. The pattern might be +1, -1, +1, -1.

Glossary

mathematical

Related to numbers and operations like addition or subtraction.

positional

Relating to the exact place or order of a letter in the alphabet.

alignment

Placing things in a straight line, like matching original letters directly over coded letters.

Recall questions

• What is the first physical step you should take when solving a coding problem?
• If vertical letter shifts don't reveal a pattern, what is the next structural pattern to check?
• How do you handle a shift operation that goes past 'Z'?

Questions & answers

If 'BEAT' is coded as 'CDBS', how is 'JUMP' coded?

KTNO

Approach: Stack BEAT and CDBS. Pattern: B(+1)=C, E(-1)=D, A(+1)=B, T(-1)=S. The rule is alternate +1, -1. Apply to JUMP: J(+1)=K, U(-1)=T, M(+1)=N, P(-1)=O.

If 'CAT' is coded as '24', what is 'DOG' coded as?

26

Approach: Substitute letters with their alphabetical positions: C(3) + A(1) + T(20) = 24. For DOG: D(4) + O(15) + G(7) = 26.

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