Each of H, U, S, B, A, N and D has an exam on a different day of a week…
2026
Each of H, U, S, B, A, N and D has an exam on a different day of a week starting from Monday and ending on Sunday of the same week. Only two people have exams between B and N. Only two people have exams between S and A. Only two people have exams between D and A. No one has an exam after D. H has an exam on one of the days before U. N has an exam immediately after U. Who has an exam on Wednesday?
Answer: C. B — ConceptIn a linear arrangement of n items over n ordered positions, a clue of the form “exactly k items lie between X and Y” fixes the distance between their…
- A.
S
- B.
D
- C.
B
- D.
H
Attempted by 18 students.
Show answer & explanation
Correct answer: C
Concept
In a linear arrangement of n items over n ordered positions, a clue of the form “exactly k items lie between X and Y” fixes the distance between their positions at k + 1, but it does not say which of the two comes first.
A clue such as “no one comes after X” pins X to the last position, and “Y is immediately after X” makes the two positions consecutive. Start from the clue that pins an absolute position, propagate the fixed distances outward from it, and use the order-only clues at the end to remove the remaining ambiguity.
Application
Number the days Monday = 1 through Sunday = 7. Each of the seven people takes exactly one day.
“No one has an exam after D” places D on day 7, Sunday.
“Only two people have exams between D and A” means the day numbers of D and A differ by 3. From D = 7 this gives A = 4, Thursday, because A = 10 falls outside the week.
“Only two people have exams between S and A” means the day numbers of S and A differ by 3. From A = 4 this gives S = 1 or S = 7; day 7 already belongs to D, so S = 1, Monday.
Days 2, 3, 5 and 6 are left for H, U, B and N. “N has an exam immediately after U” means N = U + 1, so the only consecutive pairs available are (U, N) = (2, 3) and (U, N) = (5, 6).
Test (U, N) = (2, 3). “Only two people have exams between B and N” forces B = 6, leaving H = 5. Then H would come after U, which contradicts “H has an exam on one of the days before U”, so this branch fails.
Take (U, N) = (5, 6). The same clue forces B = 3, leaving H = 2. Now H = 2 is earlier than U = 5, so “H before U” holds and every clue is satisfied.
Cross-check
Day | Person |
|---|---|
Monday | S |
Tuesday | H |
Wednesday | B |
Thursday | A |
Friday | U |
Saturday | N |
Sunday | D |
Checking every clue against this week:
A on Thursday and U on Friday lie between B on Wednesday and N on Saturday.
H on Tuesday and B on Wednesday lie between S on Monday and A on Thursday.
U on Friday and N on Saturday lie between A on Thursday and D on Sunday.
Nobody is scheduled after D on Sunday.
H on Tuesday is before U on Friday.
N on Saturday is immediately after U on Friday.
Wednesday is day 3, so B has the exam on Wednesday.