Understanding the Weekly Game Schedule Puzzle

This question requires us to determine the exact schedule of seven games (G1, G2, G3, G4, G5, G6, G7) played on seven different days of a single week, from Monday to Sunday. We are given several clues that help us deduce the order of these games.

Given Clues and Fixed Points

Let's list the clues provided:

• Seven games G1, G2, G3, G4, G5, G6, G7 played from Monday to Sunday.
• Three games were played between G2 and G5.
• Two games were played between G6 and G4.
• G3 was played on Tuesday.
• G2 was played after G4.
• G7 was played on Friday.
• G6 was played after G2.

From the clues, we have two fixed points in the schedule:

• G3 is on Tuesday.
• G7 is on Friday.

Deducing the Game Schedule

We can represent the days of the week and place the fixed games:

We know that G4 was played before G2, and G2 was played before G6 (G4 → G2 → G6 in sequence, though not necessarily on consecutive days).

Let's consider the condition: three games were played between G2 and G5.

Let's consider the condition: two games were played between G6 and G4.

We can try placing G2 based on the constraint that G4 is before it and G6 is after it. Also, G2 must have 3 days between it and G5.

• If G2 is on Wednesday, then G5 must be on Sunday (Wednesday → Thursday, Friday, Saturday → Sunday, 3 days in between). This fits the fixed G7 on Friday.
• Let's test this placement: G3 (Tue), G2 (Wed), G7 (Fri), G5 (Sun).

The schedule is shaping up:

Now, let's place G4 and G6. G4 must be before G2 (Wednesday). The only day before Wednesday that is available is Monday. So, G4 must be on Monday.

Current schedule:

Now consider the constraint: two games were played between G6 and G4. G4 is on Monday. Two games between G4 and G6 means G6 must be on Thursday (Monday → Tuesday, Wednesday → Thursday, 2 days in between). This fits the constraint that G6 is played after G2 (Wednesday).

Current schedule:

The only remaining day is Saturday and the only remaining game is G1. Therefore, G1 must be on Saturday.

The final schedule is:

Evaluating the Statements

Now let's check the given statements based on the final schedule.

Statement I: No game was played between G2 and G6.

From our schedule, G2 was played on Wednesday and G6 was played on Thursday. These are consecutive days. There are no days (and thus no games) played between Wednesday and Thursday. So, statement I is correct.

Statement II: G1 was played immediately before G5.

From our schedule, G1 was played on Saturday and G5 was played on Sunday. Saturday is immediately before Sunday. So, statement II is also correct.

Conclusion

Both Statement I and Statement II are correct based on the deduced schedule.

Revision Table: Key Constraints and Schedule

Additional Information: Logical Reasoning Tips

Solving scheduling puzzles like this one involves careful step-by-step deduction. Here are some tips:

• Start with the most concrete clues (fixed days).
• Use relative clues (before/after, number of items in between) to place elements around the fixed points.
• Look for sequences or chains of relationships (like G4 → G2 → G6).
• Try placing one element that is part of multiple constraints and see where it leads. If it creates a contradiction, backtrack and try a different placement.
• List out the available slots and items as you go.
• Always double-check your final arrangement against all the original clues to ensure everything fits.

This type of question tests your ability to combine multiple pieces of information and follow logical steps to arrive at a unique solution.