Coding-decoding: Reasoning Ability Notes for Jammu & Kashmir Patwari / Lekhpal

Coding‑Decoding (Reasoning Ability)

For the Jammu & Kashmir Patwari / Lekhpal Program (Patwari/Lekhpal Examination)

Coding: Assigning a code (a number, letter, symbol, shape, etc.) to a given item (word, figure, number, etc.) according to a hidden rule.
Decoding: Using the same rule to decode an unknown item back into the original form.

Typical format

Item (e.g., word or figure) → Code  
---------------------------------
A             →  12
B             →  34
…

Students are asked to find the missing code for a new item or the item that corresponds to a given code.

Step	Action	Example
1	Look for obvious patterns	Numbers → Sum of digits, letters → position in alphabet
2	Check for multiple attributes	Word length, number of vowels, prime numbers
3	Consider mathematical operations	Multiply, divide, square, cube, add a constant
4	Try order-based rules	1st, 2nd, 3rd…; reverse order; alternating
5	Look for hidden relationships	Word → its meaning (e.g., “SUN” → 24 because 19+21+14)
6	Confirm with all given pairs	Ensure rule works for all known items

Tip: Always test more than one rule before finalizing.

Rule	Example	Explanation
Alphabetical Position	`CAT → 3‑1‑20`	C=3, A=1, T=20
Sum of Alphabet Positions	`DOG → 4+15+7 = 26`	Sum of letters
Product of Alphabet Positions	`BAT → 2×1×20 = 40`	Product instead of sum
Number of Vowels/Consonants	`APPLE → 2 vowels → 2`	Count vowels
Length of Word	`TREE → 4`	Number of characters
Prime/Composite Check	`BIRD → 2 (prime)`	2 is the 2nd prime
Reverse Order	`HELLO → 15‑12‑12‑5‑8`	Reverse alphabet positions
Square/Cube of Position	`FIVE → 6² = 36`	6 is position of F in alphabet (6th)
Combination (Sum + Length)	`SUN → (19+21+14)+3 = 57`	Sum of letters + length
Pattern in Numbers	`1, 4, 9, 16 ...` → squares	Recognize numeric patterns
Shape/Direction Code	“↑” → 1, “→” → 2	Symbol → numeric mapping

A set of coding pairs is given:

Question: Find the code for THUNDER.

Identify a pattern
Observe the words and codes.
- Lengths: SUN(3), MOON(4), STAR(4), RAIN(4)
- Codes: 57, 73, 69, 75

Try alphabetic sums

SUN: 19+21+14 = 54 → +3 (length) = 57
MOON: 13+15+15+14 = 57 → +16 (length×4) = 73 → no consistency

Try sum + length

SUN: 54 + 3 = 57 ✔
MOON: 57 + 4 = 61 ❌

Try sum + square of length
```
SUN: 54 + 3² = 54 + 9 = 63 ❌
```
Try sum + product of length and a constant
Let's test sum + (length × 5):
```
SUN: 54 + (3×5)=54+15=69 ❌
```
Try sum + (length × 7)
```
SUN: 54 + 21 = 75 ❌
```
Try sum + (length × 2)
```
SUN: 54 + 6 = 60 ❌
```
Notice a different approach
The difference between code and sum:

Word Sum Code Code–Sum

SUN 54 57 3

MOON 57 73 16

STAR 64 69 5

RAIN 58 75 17

The differences are: 3, 16, 5, 17.
These look like length × 1, 2, 1, 4? Not consistent.

Word	Sum	Code	Code–Sum
SUN	54	57	3
MOON	57	73	16
STAR	64	69	5
RAIN	58	75	17

Try sum of squares of letters

SUN: 19²+21²+14² = 361+441+196= 998 → too large

Consider a simpler rule:
Code = Sum of letters + Number of letters × 4
```
SUN: 54 + (3×4)=54+12=66 ❌
```
Observe that
- For MOON and RAIN, the difference (Code – Sum) is +16 and +17 respectively → close to 16 and 17 (prime numbers).
- For STAR, difference is +5 → another prime