Understanding the Coding Decoding Pattern

This question involves a coding-decoding puzzle where words are coded based on a specific pattern. We are given two examples: "DICTATOR" is coded as "DROTATCI", and "GLIMPSE" is coded as "GESPMIL". We need to find the pattern and apply it to code the word "CONDEMN".

Analyzing the Examples to Find the Pattern

Let's look at the positions of the letters in the original words and their corresponding positions in the coded words.

Example 1: DICTATOR (Length = 8)

Original Word: D I C T A T O R

Positions: 1 2 3 4 5 6 7 8

Coded Word: D R O T A T C I

Positions: 1 2 3 4 5 6 7 8

Let's see which letter from the original position moves to which coded position:

• The letter at position 1 (D) moves to position 1 (D).
• The letter at position 8 (R) moves to position 2 (R).
• The letter at position 7 (O) moves to position 3 (O).
• The letter at position 4 (T) moves to position 4 (T).
• The letter at position 5 (A) moves to position 5 (A).
• The letter at position 6 (T) moves to position 6 (T).
• The letter at position 3 (C) moves to position 7 (C).
• The letter at position 2 (I) moves to position 8 (I).

So, the letter from original input position 'P' goes to coded output position 'Q'. The mapping (P → Q) for DICTATOR is:

Example 2: GLIMPSE (Length = 7)

Original Word: G L I M P S E

Positions: 1 2 3 4 5 6 7

Coded Word: G E S P M I L

Positions: 1 2 3 4 5 6 7

Let's see which letter from the original position moves to which coded position:

• The letter at position 1 (G) moves to position 1 (G).
• The letter at position 7 (E) moves to position 2 (E).
• The letter at position 6 (S) moves to position 3 (S).
• The letter at position 5 (P) moves to position 4 (P).
• The letter at position 4 (M) moves to position 5 (M).
• The letter at position 3 (I) moves to position 6 (I).
• The letter at position 2 (L) moves to position 7 (L).

The mapping (Original Position → Coded Position) for GLIMPSE is:

Identifying the Coding Pattern Rule

Let's compare the patterns for the two words based on the mapping from original position to coded position. Let N be the length of the word.

For N=8 (DICTATOR): (1→1), (2→8), (3→7), (4→4), (5→5), (6→6), (7→3), (8→2)

For N=7 (GLIMPSE): (1→1), (2→7), (3→6), (4→5), (5→4), (6→3), (7→2)

Observe the patterns:

• The letter at position 1 always goes to position 1.
• The letter at position 2 always goes to position N.
• The letter at position 3 always goes to position N-1.
• The letter at position 4 goes to position 4 (for N=8) or position 5 (for N=7).
• The letter at position 5 goes to position 5 (for N=8) or position 4 (for N=7).
• The letter at position 6 goes to position 6 (for N=8) or position 3 (for N=7).
• The letter at position 7 goes to position 3 (for N=8) or position 2 (for N=7).
• The letter at position 8 goes to position 2 (for N=8).

Let's re-frame the pattern by looking at which input position's letter goes to each output position.

Sequence of input positions that form the coded word:

For N=8 (DROTATCI from DICTATOR): The letters come from input positions 1, 8, 7, 4, 5, 6, 3, 2.

For N=7 (GESPMIL from GLIMPSE): The letters come from input positions 1, 7, 6, 5, 4, 3, 2.

Let's break down this sequence based on N:

• The 1st letter of the coded word is from Input Position 1.
• The 2nd letter is from Input Position N.
• The 3rd letter is from Input Position N-1.
• The letters for the middle positions (4 onwards) depend on N.
• The last two letters are from Input Positions 3 and 2 respectively (in the order 3, 2).

Let's look at the middle sequence of input positions (after 1, N, N-1 and before 3, 2):

• For N=8: The sequence is 4, 5, 6. These are input positions 4 up to N-2 in original order.
• For N=7: The sequence is 5, 4. These are input positions 4 up to N-2 (which are 4, 5) but reversed.

This suggests the middle part's arrangement depends on whether N is odd or even.

• If N is even (like 8), the input positions 4, 5, ..., N-2 appear in the coded word in their original order: 4, 5, ..., N-2.
• If N is odd (like 7), the input positions 4, 5, ..., N-2 appear in the coded word in reversed order: N-2, ..., 5, 4.

The complete sequence of input positions to form the coded word is:

$[1] + [N, N-1] + [\text{Positions } 4 \text{ to } N-2 \text{ (order depends on N)}] + [3, 2]$

Applying the Pattern to CONDEMN

The word "CONDEMN" has 7 letters. So, N=7. Since N=7 is odd, we apply the rule for odd length words.

Original Word: C O N D E M N

Positions: 1 2 3 4 5 6 7

The middle input positions are from 4 to N-2, which is 4 to 7-2 = 5. So the middle input positions are 4, 5.

Since N=7 is odd, we reverse the order of the middle input positions: 5, 4.

The sequence of input positions to form the coded word is:

$[1] + [N, N-1] + [\text{Middle Reversed}] + [3, 2]$

$[1] + [7, 6] + [5, 4] + [3, 2]$

The sequence of input positions is: 1, 7, 6, 5, 4, 3, 2.

Now, let's take the letters from "CONDEMN" at these positions:

• Position 1: C
• Position 7: N
• Position 6: M
• Position 5: E
• Position 4: D
• Position 3: N
• Position 2: O

Combining these letters in order gives the coded word: CNMEDNO.

Comparing this with the given options:

• CNONMED
• NMEDNOC
• NCONDEM
• CNMEDNO

The coded word "CNMEDNO" matches the fourth option.

Revision Table - Coding Patterns

Additional Information - Logical Reasoning

Coding-decoding questions are common in logical reasoning sections of competitive exams. They test your ability to observe patterns and apply rules consistently. There are many types of coding patterns, including:

• Letter Shifting: Each letter is shifted by a fixed number of positions in the alphabet (e.g., A becomes C, B becomes D).
• Reverse Order: The entire word or parts of the word are written in reverse order.
• Letter Substitution: Each letter is replaced by a specific symbol or another letter.
• Positional Rearrangement: Letters' positions are changed based on a specific rule, as seen in this problem. This rearrangement can involve simple swaps, block movements, or complex patterns based on length, position, or other factors.
• Mixed Coding: A combination of different rules might be used.

To solve coding-decoding problems:

• Carefully observe the given examples.
• Write down the original word and the coded word with their positions.
• Try to find a relationship between the original and coded letters/positions.
• Look for patterns in the first/last letters, middle letters, or segments of the word.
• Test your hypothesized pattern on all given examples.
• Once the pattern is confirmed, apply it to the word to be coded/decoded.