Question

A store sells four products — P, Q, R, and S — across four days (Mon–Thu), exactly one product per day.
P is not sold on Monday or Wednesday.
R is sold before Q.
S is not sold on Thursday.
Exactly one of P or Q is sold on Tuesday.
How many valid schedules are possible?

Hint:

When scheduling across days with ordering constraints, break the problem into cases based on the strongest restriction—here, the Tuesday condition on P and Q.

Answer 1

Correct Answer: 2

Step 1: P must be Tue or Thu (never Mon/Wed). Also Tuesday's slot must be either P or Q.
Step 2: List the three schedules that survive every rule:
(i) Mon=S, Tue=P, Wed=R, Thu=Q
(ii) Mon=R, Tue=P, Wed=S, Thu=Q
(iii) Mon=R, Tue=Q, Wed=S, Thu=P
Step 3: Verify each against all four rules (P avoids Mon/Wed; R before Q; S avoids Thu; Tue is P or Q), all three pass, and no other combination of the remaining slots does.

Total valid schedules \[ =\boxed{3} \]