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Question:

On a particular day, the pass code for the batch immediately before the rest hour was ‘bah bah black sheep have you any wool’. What was the input for the pass code on that day?

Explanation:

Here, the link of batch 2 with batch 1 and batch 3 needs to be found to solve each question. 

Denote the letters of the input by numbers 1-8 from left to right and map then for passcode of each step, as shown:

Observe that a certain movement pattern is followed by between Input and Batch 1 and a completely different pattern is followed between Batch 3 and Batch 4. 

Since there does not seem to be a correlation between the position of any number from Input up to Batch 4, there is a possibility that Input-B1 and B2-B3 follows one common pattern (say X) and B1-B2 and B3-B4 follows another common pattern (say Y). To test this, apply the B3-B4 pattern on B1 to get B2. Now, check whether applying Input-B1 on B2 gives the same outcome as B3. It does, as shown below: 

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Now, the batch timings are: Batch 1 (9:30 to 10:30); Batch 2 (10:30 to 11:30); Batch 3 (11:30 to 12:30) and Batch 4 (12:30 to 1:30). 

The period from 1:30 to 2:30 is a break, and the next batch starts again at 2:30. 

The batch just before the rest hour was batch 4. Its pass code corresponds to 75862413. Hence, the input corresponds to 12345678. 

The corresponding words are: any have wool you bah sheep bah black. 

Hence, option (b).