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Difficulty: HardCoding and Decoding

In a certain coding system, vowels are replaced by their reverse alphabetical position letters (A↔ZA \leftrightarrow Z, E↔VE \leftrightarrow V, I↔RI \leftrightarrow R, O↔LO \leftrightarrow L, U↔FU \leftrightarrow F). Consonants appearing at odd-numbered position indices (1st, 3rd, 5th, etc.) are shifted forward by 33 positions in the alphabet (+3+3), while consonants appearing at even-numbered position indices (2nd, 4th, 6th, etc.) are shifted backward by 22 positions (−2-2).

For example, under this system, the word BASKET is coded as EZVIVR.

What is the coded representation for the word HARVEST?

Answer: KZUTVQW / kzutvqw

Answer

KZUTVQW
Transforming each letter of HARVEST according to its position and type yields: Position 1 (H, odd-index consonant) →\rightarrow H +3=K+ 3 = \mathbf{K}; Position 2 (A, vowel) →\rightarrow reverse of A =Z= \mathbf{Z}; Position 3 (R, odd-index consonant) →\rightarrow R +3=U+ 3 = \mathbf{U}; Position 4 (V, even-index consonant) →\rightarrow V −2=T- 2 = \mathbf{T}; Position 5 (E, vowel) →\rightarrow reverse of E =V= \mathbf{V}; Position 6 (S, even-index consonant) →\rightarrow S −2=Q- 2 = \mathbf{Q}; Position 7 (T, odd-index consonant) →\rightarrow T +3=W+ 3 = \mathbf{W}. Concatenating these transformed letters produces KZUTVQW.

Step-by-Step Solution

1
Analyze the position index (1 to 7), letter type (vowel or consonant), and index parity (odd or even) for each letter in HARVEST.
H (1st, odd consonant), A (2nd, vowel), R (3rd, odd consonant), V (4th, even consonant), E (5th, vowel), S (6th, even consonant), T (7th, odd consonant).
Establishing individual letter rules based on position and character type is required before transformation.
2
Apply +3+3 shift to odd-positioned consonants (H, R, T).
H (8) + 3 = 11 (K); R (18) + 3 = 21 (U); T (20) + 3 = 23 (W).
Consonants at positions 1, 3, and 7 move forward by 3 letters in the alphabet.
3
Apply reverse alphabetical indexing to vowels (A, E).
A (1st letter) becomes Z (26th letter); E (5th letter) becomes V (22nd letter).
Vowels map to their opposite position pairs (27−position27 - \text{position}).$
4
Apply −2-2 shift to even-positioned consonants (V, S).
V (22) - 2 = 20 (T); S (19) - 2 = 17 (Q).
Consonants at positions 4 and 6 move backward by 2 letters in the alphabet.
5
Combine the transformed letters sequentially from positions 1 through 7.
K + Z + U + T + V + Q + W = KZUTVQW.
Assembling the converted characters in original sequence yields the final coded string.

Key Concept

Positional Parity Shift and Vowel Reverse Alphabetical Encoding
Estimated Time:2m 0s
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Topics

Coding and Decoding

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