VARC 2018 Slot 1: Logical Game Arrangement Solution
Problem Statement:
Arrange five games (A, B, C, D, E) across five days (Monday to Friday) based on the following conditions:
Game A is scheduled after Game B.
Game C is not on Monday or Friday.
Game D is on Wednesday.
Game E is scheduled before Game C.
Game B is not on Thursday.
Solution Steps:
Fix Game D on Wednesday (Condition 3).
Current Schedule:
Wednesday: D
Determine possible days for Game C (Conditions 2 & 4):
C cannot be on Monday or Friday (Condition 2).
C must be after E (Condition 4).
Possible days for C: Tuesday, Thursday.
Case 1: C on Tuesday
E must be before Tuesday → E on Monday.
Remaining days: Thursday, Friday.
Remaining games: A, B.
Condition 1 requires A > B. However, placing B on Thursday (only remaining day before Friday) violates Condition 5 (B ≠ Thursday).
Conclusion: Invalid Case.
Case 2: C on Thursday
E must be before Thursday → E can be Monday or Tuesday.
Subcase 2a: E on Monday
Remaining days: Tuesday, Friday.
Remaining games: A, B.
Condition 1 (A > B) → Place B on Tuesday and A on Friday.
Final Schedule:
Monday: E
Tuesday: B
Wednesday: D
Thursday: C
Friday: A
Validation:
All conditions are satisfied.
Answer:
The games are scheduled as follows:
Monday: E
Tuesday: B
Wednesday: D
Thursday: C
Friday: A
Final Schedule:
E → B → D → C → A
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