Understanding the Logic Puzzle: Coaches, Games, and Days

This is a logic puzzle involving seven coaches, seven different games, and seven days of the week. Each coach is associated with exactly one game and trains on exactly one day, with no two coaches training on the same day.

We are given several clues to determine the schedule of each coach. Let's break down the clues and use them to build the complete schedule.

Breaking Down the Clues

Here are the pieces of information provided:

• There are 7 coaches: A, B, C, D, E, F, and G.
• There are 7 games: Hockey, Cricket, Badminton, Tennis, Volleyball, Basketball, and Football.
• There are 7 days: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday.
• Clue 1: C trains Badminton on Friday.
• Clue 2: B teaches Volleyball on the previous day of the day on which a coach trains Hockey. This means Volleyball is on DayX and Hockey is on DayX+1 for some consecutive days.
• Clue 3: G trains on Sunday but does not train Cricket or Tennis.
• Clue 4: D trains Basketball on the previous day of the day on which F trains. This means Basketball is on DayY (for D) and F trains on DayY+1 for some consecutive days.
• Clue 5: A trains Football on Tuesday.
• Clue 6: E does not train Tennis.

Building the Schedule Step-by-Step

Let's use a table to keep track of the assignments for each day.

Let's fill in the direct clues:

• From Clue 1, C trains Badminton on Friday.
• From Clue 5, A trains Football on Tuesday.
• From Clue 3, G trains on Sunday.

Now consider Clue 3 again: G is on Sunday and does not train Cricket or Tennis. The games are Hockey, Cricket, Badminton, Tennis, Volleyball, Basketball, Football. Badminton (C) and Football (A) are taken. So G (Sunday) can be Hockey, Volleyball, or Basketball.

We have two pairs of coaches training on consecutive days:

• Pair 1: B (Volleyball) and the coach training Hockey (on the next day).
• Pair 2: D (Basketball) and F (on the next day).

Let's look at the days: Monday, Tuesday(A), Wednesday, Thursday, Friday(C), Saturday, Sunday(G). The occupied days are Tuesday, Friday, and Sunday. The available days are Monday, Wednesday, Thursday, and Saturday.

We need two sets of consecutive days for the pairs. Let's examine possible consecutive day pairs from the whole week, considering occupied slots:

• (Mon, Tue): Tue is A. A is not part of these pairs. Not possible.
• (Tue, Wed): Tue is A. A is not part of these pairs. Not possible.
• (Wed, Thu): Both days are available. This is a possible slot for either pair.
• (Thu, Fri): Fri is C. C is not part of these pairs. Not possible.
• (Fri, Sat): Fri is C. C is not part of these pairs. Not possible.
• (Sat, Sun): Sat is available, Sun is G. Could this be a pair? If this is (B-Volleyball, Hockey), then B is on Sat and Hockey is on Sun. If Hockey is on Sun, the coach on Sunday (G) must train Hockey. This fits G's condition (G on Sunday, not Cricket/Tennis). So, B(Volleyball)-Saturday and G(Hockey)-Sunday is a possible assignment.
• (Sun, Mon): Sun is G. G is not part of the first day of these pairs (B or D). Not possible.

So, we have two potential consecutive slots for the two pairs: (Wed, Thu) and (Sat, Sun). Since we need two pairs, one must take (Wed, Thu) and the other must take (Sat, Sun).

Based on our analysis above, only one pair could potentially use (Sat, Sun): B(Volleyball) on Saturday and G(Hockey) on Sunday. Let's assign this first as it also determines G's game.

• B trains Volleyball on Saturday.
• G trains Hockey on Sunday.

Now let's place the second consecutive pair: D (Basketball) on DayY, F on DayY+1. The remaining available days are Monday, Wednesday, and Thursday. The only consecutive pair within these days is (Wed, Thu).

• D trains Basketball on Wednesday.
• F trains on Thursday.

We have now placed coaches A, B, C, D, F, and G. The remaining coach is E. We have assigned days Tuesday, Wednesday, Thursday, Friday, Saturday, and Sunday. The remaining day is Monday. So, E trains on Monday.

Now let's determine the remaining games. The games assigned are Football (A), Badminton (C), Volleyball (B), Hockey (G), and Basketball (D). The remaining games are Cricket and Tennis. These must be assigned to E (on Monday) and F (on Thursday).

Clue 6 states that E does not train Tennis. Since E trains on Monday and the remaining games for E and F are Cricket and Tennis, E must train Cricket on Monday.

This leaves Tennis as the only remaining game, which must be assigned to F on Thursday.

Let's verify all clues against this final schedule:

• C trains Badminton on Friday: Yes.
• B trains Volleyball on the previous day of Hockey: B(Volleyball) on Saturday, G(Hockey) on Sunday. Yes.
• G trains on Sunday but not Cricket or Tennis: G(Hockey) on Sunday. Yes.
• D trains Basketball on the previous day of F: D(Basketball) on Wednesday, F(Tennis) on Thursday. Yes.
• A trains Football on Tuesday: Yes.
• E does not train Tennis: E trains Cricket. Yes.

The schedule is consistent with all clues.

Answering the Question: On which day does F train?

Looking at the final schedule table, F trains on Thursday.

Revision Table: Coach, Game, and Day Assignments

Additional Information: Logic Puzzle Strategies

Logic puzzles like this one require careful deduction and organization. Some helpful strategies include:

• Reading all clues first to get an overview.
• Identifying direct assignments that fix a specific item (like C on Friday, A on Tuesday, G on Sunday).
• Using tables or grids to keep track of possibilities and eliminations.
• Focusing on clues that link multiple items (like the consecutive day pairs).
• Testing possibilities systematically when direct assignments aren't immediately obvious. If a possibility leads to a contradiction, discard it and try another.
• Checking all conditions against the final solution to ensure accuracy.

These puzzles test logical reasoning and attention to detail, skills important for many competitive exams.