Decoding the Coding Pattern

The question presents a coding relationship: ADVENTURES is coded as VDANEUTSER. The task is to determine this coding logic and apply it to the word SYSTEMATIC.

Step 1: Analyze the Example Word

The example word ADVENTURES has 10 letters. It can be divided into two equal halves:

• First Half: ADVEN (Letters 1-5)
• Second Half: TURES (Letters 6-10)

The coded word VDANEUTSER also has 10 letters and can be divided similarly:

• First Coded Half: VDANE
• Second Coded Half: UTSER

Step 2: Identify Rearrangement Patterns

Examine the transformation of the first half:

• Original ADVEN (Indices: A₁ D₂ V₃ E₄ N₅)
• Coded VDANE (Letters from original indices: 3, 2, 1, 5, 4)

The pattern for the first half is a specific rearrangement: the 3rd letter comes first, the 2nd stays second, the 1st comes third, the 5th comes fourth, and the 4th comes fifth. Pattern: (3, 2, 1, 5, 4).

Examine the transformation of the second half:

• Original TURES (Indices: T₆ U₇ R₈ E₉ S₁₀)
• Coded UTSER (Letters from original indices: 7, 6, 10, 9, 8)

The pattern for the second half involves rearranging the letters based on their original positions: the 7th letter first, then the 6th, then the 10th, then the 9th, and finally the 8th. Pattern: (7, 6, 10, 9, 8).

Step 3: Apply Patterns to SYSTEMATIC

The target word is SYSTEMATIC, which has 10 letters. Split it into two halves:

• First Half: SYSTE (Letters 1-5)
• Second Half: MATIC (Letters 6-10)

Applying First Half Pattern

Rearrange SYSTE using the pattern (3, 2, 1, 5, 4):

• Original: S₁ Y₂ S₃ T₄ E₅
• Applying pattern (3, 2, 1, 5, 4): S₃ Y₂ S₁ E₅ T₄
• Resulting First Half: SYSET

Applying Second Half Pattern

Rearrange MATIC using the pattern derived from the second half (7, 6, 10, 9, 8). These indices refer to the positions within the 10-letter word SYSTEMATIC.

• Original: M₆ A₇ T₈ I₉ C₁₀
• Applying pattern (7, 6, 10, 9, 8): A₇ M₆ C₁₀ I₉ T₈
• Resulting Second Half: AMCIT

Step 4: Combine Coded Halves

Combine the rearranged halves to form the final coded word:

• First Coded Half: SYSET
• Second Coded Half: AMCIT
• Combined: SYSETAMCIT

Conclusion

Following the identified coding pattern, SYSTEMATIC is coded as SYSETAMCIT.