Each of E, F, G, I, K, L and M has an exam on a different day of a week,…
2026
Each of E, F, G, I, K, L and M has an exam on a different day of a week, starting from Monday and ending on Sunday of the same week. F has an exam on Friday. Only two people have exams between K and F. Only four people have exams between E and K. L has an exam immediately after G. I does not have an exam on Monday. How many people have exams between I and M?
Answer: B. Four — Concept — On a fixed day-line of seven positions, a clue of the form "only n people are between X and Y" fixes nothing but the distance between their…
- A.
One
- B.
Four
- C.
Three
- D.
Two
Attempted by 28 students.
Show answer & explanation
Correct answer: B
Concept — On a fixed day-line of seven positions, a clue of the form "only n people are between X and Y" fixes nothing but the distance between their positions: the two day-numbers differ by n + 1. Such a clue never says which of the two comes first, so both directions are tested and only the placement that stays inside Monday to Sunday survives. The method is therefore to anchor on the single clue that names a real day, propagate every distance clue outward from that anchor, and fill the leftover days with the adjacency and negative clues.
Application
Number the days Monday = 1, Tuesday = 2, Wednesday = 3, Thursday = 4, Friday = 5, Saturday = 6, Sunday = 7. F has an exam on Friday, so F sits at position 5. This is the anchor.
"Only two people have exams between K and F" means the distance is 2 + 1 = 3, so K sits at 5 - 3 = 2 or at 5 + 3 = 8. Position 8 lies outside the week, so K sits at position 2, Tuesday.
"Only four people have exams between E and K" means the distance is 4 + 1 = 5, so E sits at 2 + 5 = 7 or at 2 - 5 = -3. Only position 7 exists, so E sits at position 7, Sunday.
The still-free positions are 1, 3, 4 and 6 (Monday, Wednesday, Thursday, Saturday) for G, I, L and M. "L has an exam immediately after G" needs two consecutive free positions, and 3 and 4 are the only consecutive pair left. So G sits at position 3, Wednesday, and L at position 4, Thursday.
Positions 1 and 6 (Monday and Saturday) remain for I and M. I does not have an exam on Monday, so I takes position 6, Saturday, and M takes position 1, Monday.
I is at position 6 and M is at position 1. The distance is 6 - 1 = 5, so the count of people strictly between them is 5 - 1 = 4: the exams at positions 2, 3, 4 and 5, which belong to K, G, L and F.
Cross-check — The completed schedule, and every clue read back against it:
Day | Person |
|---|---|
Monday | M |
Tuesday | K |
Wednesday | G |
Thursday | L |
Friday | F |
Saturday | I |
Sunday | E |
F has an exam on Friday, exactly as given.
Between K (Tuesday) and F (Friday) lie Wednesday and Thursday, which is two people, G and L.
Between E (Sunday) and K (Tuesday) lie Wednesday, Thursday, Friday and Saturday, which is four people, G, L, F and I.
L (Thursday) has an exam immediately after G (Wednesday).
I has an exam on Saturday, so not on Monday.
Every clue holds, and no other schedule satisfies all of them, so exactly four people, K, G, L and F, have exams between I and M.