Pochu and Puchu were caught talking in the class by their class teacher Mrs. Ruplekha Banerjee. Pochu smiled innocently and got away with it. Puchu apologized and said that she was discussing the weekly class schedule. Since Mrs. Banerjee wanted to know if Puchu was saying the truth, she drew a table with 3 columns. The 1st column had days of the week from Monday to Saturday, the 2nd was to be filled with names of teachers and the 3rd was to be filled with names of the subjects that each one of them taught. She then asked Puchu to fill this table with the name of the 1st lecture for each day of the week along with the respective name of the teacher teaching that subject and went to attend a call.
Puchu knew the following information:
- The school held classes on 6 days of the week. Every day started with a different subject taught by a different teacher.
- There were only 6 subjects and only 6 teachers who taught their class.
- The subjects were English, Mathematics, History, Geography, Science, Physical Education.
- The teachers were Mrs. Prerna, Mrs. Ruplekha, Mrs. Quinea, Mrs. Neha, Mrs. Veena, Mrs. Xinia.
When Mrs. Banerjee was talking over the phone, Puchu asked her favourite teacher Mrs. Shohini Dasgupta for help. Officially, Mrs. Dasgupta could not help Puchu directly. Since Puchu was her favourite student, Mrs. Shohini gave her some clues to help her fill the table. Mrs. Shohini said the following: - Convert the name of each teacher as well as subject to a number. This number would be the position of the 1st letter of the name of the teacher or subject in the alphabet.
- The subject and the teacher who have a perfect square number are on the extreme days of the week, but not on the same day.
- A pair of consecutive numbers appears on the same day, with the smaller one appearing in column II. Both of them appear on Wednesday.
- If we consider all 7 days of the week starting with Monday, then the biggest number, and the number that is a perfect cube are both in the middle of the week.
- Two 2-digit prime numbers are in the same row of the table.
- Mrs. Neha does not teach Mathematics but teaches on Saturday.
- A single digit number (not a factor of 37 × 105) and another number (twice a prime number greater than 10) are in the same row of the table.
- The numbers in the 2 columns cannot be the same for any particular day.
At this instant, Mrs. Banerjee came back in the class, and Mrs. Shohini had to stop. Find the probability that Puchu can fill the table without any error, if she deciphers each given clue correctly.
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