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Question

Each of T, R, O, U, B, L and E has an exam on a different day of a week starting from Monday and ending on Sunday of the same week. Only three people have exam between L and T. Only three people have exam between U and O. B has exam on some day before E and on some day after R. Only O has exam after T. How many people have exam after B?

The correct answer is
Three

We need to determine the number of people who have an exam after B. To solve this, let's assign the days of the week to each person based on the given constraints. Here's the step-by-step reasoning:

  1. Consider the seven days of the week starting from Monday to Sunday: M, T, W, Th, F, Sa, Su.
  2. We are given that only three people have exams between L and T. This suggests two possible arrangements:
    • L, _, _, _, T
    • T, _, _, _, L
  3. Only three people have exams between U and O. This suggests two possible arrangements:
    • U, _, _, _, O
    • O, _, _, _, U
  4. B is between R and E, where B has an exam after R and before E. This is key to arranging these individuals.
  5. Only O has an exam after T. Thus, O is the last to have an exam.

Given these data points, let's try to position everyone:

  • If T is on Monday, then L is on Friday (since three people are between L and T).
  • If U is on Tuesday, then O must be on Saturday (since three people are between U and O).
  • If R is on Wednesday, then B could be on Thursday and E on Sunday (since B must be after R and E after B).

The order now becomes:

MondayTuesdayWednesdayThursdayFridaySaturdaySunday
TURBLOE

Now, let's count the number of people having exams after B on Thursday:

  • Friday: L
  • Saturday: O
  • Sunday: E

Thus, there are three people who have exams after B.

Therefore, the correct answer is: Three.

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Important Questions from Scheduling Puzzle

  1. P, Q, R, S, T, U and V have an exam on different days of the week starting on Monday and ending on Sunday. Q has an exam on Friday. Exactly 3 people have an exam between R and T, neither of whom has on exam on Sunday. P has an exam immediately after U. V has an exam immediately before T. Who among the following has an exam on Wednesday?
  2. Each of P, Q, R, S, T, U and V has an exam on a different day of a week starting from Monday and ending on Sunday of the same week. V has an exam on Tuesday. Exactly 2 people have an exam between V and P. S has an exam immediately before T, and Q has an exam immediately after R. Only 1 person has an exam between T and R
    How many people have an exam before S?

  3. Each of P, Q, R, S, T, U and V has an exam on a different day of a week starting from Monday and ending on Sunday of the same week. Only five people have exams between T and Q. U has an exam on Thursday. S has an exam immediately after Q. R has an exam immediately after P. How many people have exams between V and T?

  4. P, Q, R, S, T, U and V have an exam on different days of the week starting on Monday and ending on Sunday. Q has an exam on Wednesday. Exactly 4 people have an exam between T and U, neither of whom has an exam on Monday. R has an exam immediately before S and V has an exam immediately after S. P has an exam immediately before T.
    How many people have an exam between P and R?

  5. Each of P, Q, R, S, T, U and V has an exam on a different day of a week starting from Monday and ending on Sunday of the same week. V has an exam on Thursday. Exactly 4 people have their exams between U and Q, neither of whom has an exam on Sunday. T has an exam immediately before S. R does not have an exam on Friday. U does not have an exam after S. How many people have exams after Q?
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