Students Admission Schedule Deduction

This problem requires us to determine the admission schedule for seven students (J, K, L, M, N, O, P) over seven days of a week (Monday to Sunday) based on a set of clues. Once the schedule is figured out, we need to count how many students are admitted between student K and student O.

Schedule Step-by-Step Analysis

Let's break down the clues to build the schedule:

• Clue 1 & 2: "Two students take admission between K and N. K takes admission before N." This establishes a sequence: K, Student, Student, N.
• Clue 4: "J takes admission on Wednesday." This places J on Wednesday.
• Clue 5 & 6: "Only one student takes admission between J and M" and "L takes admission before M and after K" (K ... L ... M).

  Since J is on Wednesday, and only one student is between J and M, M must be on Friday (J on Wed, Student on Thu, M on Fri). This arrangement also requires K and L to be admitted before Friday, with K before L (K ... L ... M). This means K must be on Monday and L on Tuesday.

  The schedule so far:

  Monday: K
  Tuesday: L
  Wednesday: J
  Thursday: Student between J & M
  Friday: M

• Using Clues 1 & 2 again: With K admitted on Monday, the sequence K, Student, Student, N implies that N must be admitted on Thursday.
• Updating Schedule:

  Monday: K
  Tuesday: L
  Wednesday: J
  Thursday: N
  Friday: M

• Clue 3: "O takes admission in one of the day after M." M is on Friday, so O must be admitted on Saturday or Sunday.
• Remaining Students & Days: The remaining students are O and P. The remaining days are Saturday and Sunday.
• Clue 7: "P does not take admission on Sunday." This means P must be admitted on Saturday. Consequently, O must be admitted on Sunday.

Admission Schedule Finalized

Based on the deductions, the complete admission schedule is as follows:

Admissions Between K and O Calculation

Now, let's find the number of students admitted between K and O.

• Student K is admitted on Monday (Day $1$).
• Student O is admitted on Sunday (Day $7$).
• The students admitted on the days between Day $1$ and Day $7$ are those admitted on Day $2$, Day $3$, Day $4$, Day $5$, and Day $6$.
• These students are L, J, N, M, and P.
• Counting these students, we find there are 5 students. This number can be represented as $5$.

Comparing this count with the given options:

• Three
• Two
• None
• One
• More than three

Since $5$ is greater than $3$, the correct option is 'More than three'.