Understanding the Letter Cluster Pattern

The question asks us to find a pattern in how letter clusters are transformed. We need to figure out the rule connecting the first pair (CURTAIN : RUCTNIA) and apply it to find the transformation for TONIGHT, given the second pair (SUPPOSE : PUSPESO) also follows the same rule.

Decoding the Transformation Rule for CURTAIN

Let's first analyze the relationship between CURTAIN and RUCTNIA.

The word CURTAIN has 7 letters. We can denote their positions using numbers:

C₁ U₂ R₃ T₄ A₅ I₆ N₇

The transformed cluster is RUCTNIA. Let's identify the original position of each letter in the new cluster:

• The 1st letter of RUCTNIA is 'R', which was the 3rd letter of CURTAIN.
• The 2nd letter of RUCTNIA is 'U', which was the 2nd letter of CURTAIN.
• The 3rd letter of RUCTNIA is 'C', which was the 1st letter of CURTAIN.
• The 4th letter of RUCTNIA is 'T', which was the 4th letter of CURTAIN.
• The 5th letter of RUCTNIA is 'N', which was the 7th letter of CURTAIN.
• The 6th letter of RUCTNIA is 'I', which was the 6th letter of CURTAIN.
• The 7th letter of RUCTNIA is 'A', which was the 5th letter of CURTAIN.

This indicates a specific rearrangement based on the original positions. If we represent the original sequence of positions as $P_{orig} = (1, 2, 3, 4, 5, 6, 7)$, the sequence of positions in the transformed cluster is $P_{new} = (3, 2, 1, 4, 7, 6, 5)$.

Verifying the Rule with SUPPOSE

To confirm our derived rule, let's apply it to the second pair: SUPPOSE : PUSPESO.

The letters of SUPPOSE are at positions:

S₁ U₂ P₃ P₄ O₅ S₆ E₇

Using the positional rule $P_{new} = (3, 2, 1, 4, 7, 6, 5)$, we rearrange the letters:

• The 3rd letter of SUPPOSE is 'P'.
• The 2nd letter is 'U'.
• The 1st letter is 'S'.
• The 4th letter is 'P'.
• The 7th letter is 'E'.
• The 6th letter is 'S'.
• The 5th letter is 'O'.

Combining these gives us PUSPESO. This perfectly matches the transformation provided for the second pair, confirming our rule is accurate.

Applying the Rule to TONIGHT

Now we apply the same positional rearrangement rule, $P_{new} = (3, 2, 1, 4, 7, 6, 5)$, to the word TONIGHT.

The letters of TONIGHT and their positions are:

T₁ O₂ N₃ I₄ G₅ H₆ T₇

Rearranging according to the rule $P_{new} = (3, 2, 1, 4, 7, 6, 5)$:

• The 3rd letter is 'N'.
• The 2nd letter is 'O'.
• The 1st letter is 'T'.
• The 4th letter is 'I'.
• The 7th letter is 'T'.
• The 6th letter is 'H'.
• The 5th letter is 'G'.

Putting these rearranged letters together results in the cluster: NOTITHG.

Selecting the Correct Option

The result we obtained is NOTITHG. Comparing this with the options provided:

1. NOTITGH
2. NOTITHG
3. NTOITGH
4. NOTIHTG

Our calculated transformation, NOTITHG, matches exactly with option 2.