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Introduction
Mathematical Coding problems map numbers or words to numeric codes using a clear arithmetic rule - for example, squares, cubes, products, sums, differences, factorial-based transforms, or combinations of positions and arithmetic operations.
This pattern is important because it trains you to recognise numeric relationships quickly and translate those relationships into a consistent coding rule - a frequent requirement in reasoning and quantitative sections.
Pattern: Mathematical Coding
The key concept is: the numeric code is generated by applying a consistent arithmetic operation (or combination of operations) to the input value(s). Examples include n², n³, product of digits, sum of positions, difference between extremes, factorial-based values, or combinations like (first×last)+(middle).
Things to check when you see a numeric code:
- Is the code a power (square, cube)? (e.g., 2→4, 3→9, 4→16)
- Is it a product of digits or positions? (e.g., 14 → 1×4 =4)
- Is it a sum/difference of letter positions? (A=1…Z=26)
- Does it use concatenation of sub-results? (e.g., product then sum → 12|3 → 123)
- Is there modulo reduction / normalization (e.g., reduce to 1-26)?
Step-by-Step Example
Question
In a certain code:
2 → 8, 3 → 27, 4 → 64. What is the code for 5?
Solution
-
Step 1: Observe the pattern
The given mappings are 2→8, 3→27, 4→64. These match perfect cubes: 2³=8, 3³=27, 4³=64. So the rule appears to be code = n³ (cube of the number). -
Step 2: Apply the rule to 5
5³ = 5×5×5 = 125. -
Final Answer:
125 -
Quick Check:
Reverse-check: cube-root of 125 = 5. Pattern consistent with examples (2³,3³,4³) ✅
Quick Variations
1. Power rules: n², n³, n⁴.
2. Digit-based: sum of digits, product of digits, difference between digits.
3. Position-sum: for words, sum letter positions (A=1 … Z=26).
4. Composite rules: combine operations such as (sum × product), (first² + last), or (n! / k).
5. Concatenation: compute two small results and join them (e.g., sum=7, product=12 → code 712).
Trick to Always Use
- Step 1: Compute simple transforms first - square, cube, factorial, sum, product - and see if any match exactly.
- Step 2: If not exact, check for combinations (sum of positions, product of extremes, concatenation of sub-results).
- Step 3: Watch for normalization (mod 26) or trimming (keeping last two digits) if numbers seem large.
- Step 4: Always perform a quick reverse-check: apply inverse operation (root, division, subtraction) to confirm consistency.
Summary
- Identify if the given mapping follows a basic arithmetic rule (square, cube, factorial, etc.).
- Check if the pattern uses digit-based logic like sum, product, or difference.
- Look for composite or concatenated rules such as (sum × product) or (first² + last).
- Always reverse-check the rule to confirm consistency before finalizing the answer.
Example to remember:
If 2 → 8, 3 → 27, 4 → 64, then 5 → 125 (Cube rule).