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Puzzles Competition | CAT 2025 Slot 3 DILR | Scheduling based Puzzle | Medium

Puzzles Competition | CAT 2025 Slot 3 DILR | Scheduling based Puzzle | Medium


Anirbid, Chandranath, Koushik, and Suranjan participated in a puzzle solving competition. The competition comprised 10 puzzles that had to be solved in the same sequence, i.e., a competitor got access to a puzzle as soon as they solved the previous puzzle. Some of the puzzles were visual puzzles and the others were number-based puzzles. The winner of the competition was the one who solved all puzzles in the least time.

The following charts describe their progress in the competition. The chart on the left shows the number of puzzles solved by each competitor at a given time (in minutes) after the start of the competition. The chart on the right shows the number of visual puzzles solved by each competitor at a given time (in minutes) after the start of the competition.

Who had solved the largest number of puzzles by the 20-th minute from the start of the competition?

1. Suranjan

2. Koushik

3. Anirbid

4. Chandranath

Answer & Explanation

Correct Answer: Koushik

Explanation: Can be solved visually from the graph. At 20th minute Kaushik is on the top with maximum puzzles solved.

From the final completion table, we check how many puzzles each competitor had completed by the 20th minute. Anirbid completes puzzle 5 at 19 minutes and puzzle 6 only at 22 minutes, so he has solved 5 puzzles by 20 minutes. Chandranath also finishes puzzle 5 at 17 minutes and reaches puzzle 6 at 21 minutes, giving him 5 puzzles by 20 minutes. Koushik, however, completes puzzle 7 at 19 minutes and reaches puzzle 8 only at 25 minutes, so he has already solved 7 puzzles by the 20th minute. Suranjan completes only puzzle 4 by 18 minutes and reaches puzzle 5 at 21 minutes, so he has solved 4 puzzles by 20 minutes. Since 7 is the maximum among all competitors, Koushik has solved the largest number of puzzles.

The graphs converted to table for ease of understanding

Final Puzzle Completion Time Table (Time in Minutes)

Puzzles SolvedAnirbid (Red)Chandranath (Yellow)Koushik (Green)Suranjan (Blue)
14425
29647
31110712
414131218
519171421
622211623
727231926
829262528
933282930
1037303135

Visual Puzzles Completion Times (Time in Minutes)

Order of CompletionAnirbidChandranathKoushikSuranjan
1st Visual Puzzle4425
2nd Visual Puzzle14131218
3rd Visual Puzzle29262528
4th Visual Puzzle33282930

Step 0 – Start with a blank skeleton

Clue used: We know there are 10 puzzles and 4 competitors, and we ultimately want: Puzzle #, Type (V/N), Index (V1, N3, etc.), and completion times.

Blank structure:

Puzzle #TypeIndexAnirbidChandranathKoushikSuranjan
1
2
3
4
5
6
7
8
9
10

 

Step 1 – Fill completion times from “Total Puzzles Solved” table

Clue used:
The “Final Puzzle Completion Time” table gives, for each competitor, the time when each puzzle was completed.

We just copy those times row-wise.

Puzzle #TypeIndexAnirbidChandranathKoushikSuranjan
14425
29647
31110712
414131218
519171421
622211623
727231926
829262528
933282930
1037303135

No calculations yet, just transcription.

Step 2 – Identify which puzzle numbers are Visual (using Koushik)

Clue used:
From the Visual Puzzles Completion Times for Koushik:

  • 1st visual at 2 min
  • 2nd visual at 12 min
  • 3rd visual at 25 min
  • 4th visual at 29 min

Compare these with Koushik’s total completion times:

  • Puzzle 1 = 2 min → matches 1st visual → Puzzle 1 is Visual (V).
  • Puzzle 4 = 12 min → matches 2nd visual → Puzzle 4 is V.
  • Puzzle 8 = 25 min → matches 3rd visual → Puzzle 8 is V.
  • Puzzle 9 = 29 min → matches 4th visual → Puzzle 9 is V.

Fill Type = V in those rows; others will be N.

Puzzle #TypeIndexAnirbidChandranathKoushikSuranjan
1V4425
2N9647
3N1110712
4V14131218
5N19171421
6N22211623
7N27231926
8V29262528
9V33282930
10N37303135

 

Step 3 – Assign V and N indices (Index column)

Clue used: We now know the order of all Visual and Number puzzles:

  • Types in order: V, N, N, V, N, N, N, V, V, N

We walk from Puzzle 1 to 10 and count:

  • Puzzle 1: first Visual → V1
  • Puzzle 2: first Number → N1
  • Puzzle 3: second Number → N2
  • Puzzle 4: second Visual → V2
  • Puzzle 5: third Number → N3
  • Puzzle 6: fourth Number → N4
  • Puzzle 7: fifth Number → N5
  • Puzzle 8: third Visual → V3
  • Puzzle 9: fourth Visual → V4
  • Puzzle 10: sixth Number → N6

Now fill the Index column:

Puzzle #TypeIndexAnirbidChandranathKoushikSuranjan
1VV14425
2NN19647
3NN21110712
4VV214131218
5NN319171421
6NN422211623
7NN527231926
8VV329262528
9VV433282930
10NN637303135

How many minutes did Suranjan take to solve the third visual puzzle in the competition?

Answer & Explanation

Correct Answer: 2

Explanation: The question asks for the time Suranjan took to solve the third visual puzzle, meaning the duration spent on that puzzle alone. From the fixed sequence, the third visual puzzle corresponds to overall puzzle number 8. Suranjan completes puzzle 7 at 26 minutes and puzzle 8 at 28 minutes. As puzzles are solved sequentially, the time taken for puzzle 8 is the difference between these two times. Therefore, the time spent on the third visual puzzle is 28 minus 26, which equals 2 minutes.

The graphs converted to table for ease of understanding

Final Puzzle Completion Time Table (Time in Minutes)

Puzzles SolvedAnirbid (Red)Chandranath (Yellow)Koushik (Green)Suranjan (Blue)
14425
29647
31110712
414131218
519171421
622211623
727231926
829262528
933282930
1037303135

Visual Puzzles Completion Times (Time in Minutes)

Order of CompletionAnirbidChandranathKoushikSuranjan
1st Visual Puzzle4425
2nd Visual Puzzle14131218
3rd Visual Puzzle29262528
4th Visual Puzzle33282930

Step 0 – Start with a blank skeleton

Clue used: We know there are 10 puzzles and 4 competitors, and we ultimately want: Puzzle #, Type (V/N), Index (V1, N3, etc.), and completion times.

Blank structure:

Puzzle #TypeIndexAnirbidChandranathKoushikSuranjan
1
2
3
4
5
6
7
8
9
10

 

Step 1 – Fill completion times from “Total Puzzles Solved” table

Clue used:
The “Final Puzzle Completion Time” table gives, for each competitor, the time when each puzzle was completed.

We just copy those times row-wise.

Puzzle #TypeIndexAnirbidChandranathKoushikSuranjan
14425
29647
31110712
414131218
519171421
622211623
727231926
829262528
933282930
1037303135

No calculations yet, just transcription.

Step 2 – Identify which puzzle numbers are Visual (using Koushik)

Clue used:
From the Visual Puzzles Completion Times for Koushik:

  • 1st visual at 2 min
  • 2nd visual at 12 min
  • 3rd visual at 25 min
  • 4th visual at 29 min

Compare these with Koushik’s total completion times:

  • Puzzle 1 = 2 min → matches 1st visual → Puzzle 1 is Visual (V).
  • Puzzle 4 = 12 min → matches 2nd visual → Puzzle 4 is V.
  • Puzzle 8 = 25 min → matches 3rd visual → Puzzle 8 is V.
  • Puzzle 9 = 29 min → matches 4th visual → Puzzle 9 is V.

Fill Type = V in those rows; others will be N.

Puzzle #TypeIndexAnirbidChandranathKoushikSuranjan
1V4425
2N9647
3N1110712
4V14131218
5N19171421
6N22211623
7N27231926
8V29262528
9V33282930
10N37303135

 

Step 3 – Assign V and N indices (Index column)

Clue used: We now know the order of all Visual and Number puzzles:

  • Types in order: V, N, N, V, N, N, N, V, V, N

We walk from Puzzle 1 to 10 and count:

  • Puzzle 1: first Visual → V1
  • Puzzle 2: first Number → N1
  • Puzzle 3: second Number → N2
  • Puzzle 4: second Visual → V2
  • Puzzle 5: third Number → N3
  • Puzzle 6: fourth Number → N4
  • Puzzle 7: fifth Number → N5
  • Puzzle 8: third Visual → V3
  • Puzzle 9: fourth Visual → V4
  • Puzzle 10: sixth Number → N6

Now fill the Index column:

Puzzle #TypeIndexAnirbidChandranathKoushikSuranjan
1VV14425
2NN19647
3NN21110712
4VV214131218
5NN319171421
6NN422211623
7NN527231926
8VV329262528
9VV433282930
10NN637303135

At what number in the sequence was the fourth number-based puzzle?

Answer & Explanation

Correct Answer: 6

Explanation: From the fixed puzzle sequence, visual puzzles occur at positions 1, 4, 8, and 9. Hence, the number-based puzzles are at positions 2, 3, 5, 6, 7, and 10. Counting the number-based puzzles in order, the first is at position 2, the second at position 3, the third at position 5, and the fourth at position 6. Therefore, the fourth number-based puzzle appears as the sixth puzzle in the overall sequence.

The graphs converted to table for ease of understanding

Final Puzzle Completion Time Table (Time in Minutes)

Puzzles SolvedAnirbid (Red)Chandranath (Yellow)Koushik (Green)Suranjan (Blue)
14425
29647
31110712
414131218
519171421
622211623
727231926
829262528
933282930
1037303135

Visual Puzzles Completion Times (Time in Minutes)

Order of CompletionAnirbidChandranathKoushikSuranjan
1st Visual Puzzle4425
2nd Visual Puzzle14131218
3rd Visual Puzzle29262528
4th Visual Puzzle33282930

Step 0 – Start with a blank skeleton

Clue used: We know there are 10 puzzles and 4 competitors, and we ultimately want: Puzzle #, Type (V/N), Index (V1, N3, etc.), and completion times.

Blank structure:

Puzzle #TypeIndexAnirbidChandranathKoushikSuranjan
1
2
3
4
5
6
7
8
9
10

 

Step 1 – Fill completion times from “Total Puzzles Solved” table

Clue used:
The “Final Puzzle Completion Time” table gives, for each competitor, the time when each puzzle was completed.

We just copy those times row-wise.

Puzzle #TypeIndexAnirbidChandranathKoushikSuranjan
14425
29647
31110712
414131218
519171421
622211623
727231926
829262528
933282930
1037303135

No calculations yet, just transcription.

Step 2 – Identify which puzzle numbers are Visual (using Koushik)

Clue used:
From the Visual Puzzles Completion Times for Koushik:

  • 1st visual at 2 min
  • 2nd visual at 12 min
  • 3rd visual at 25 min
  • 4th visual at 29 min

Compare these with Koushik’s total completion times:

  • Puzzle 1 = 2 min → matches 1st visual → Puzzle 1 is Visual (V).
  • Puzzle 4 = 12 min → matches 2nd visual → Puzzle 4 is V.
  • Puzzle 8 = 25 min → matches 3rd visual → Puzzle 8 is V.
  • Puzzle 9 = 29 min → matches 4th visual → Puzzle 9 is V.

Fill Type = V in those rows; others will be N.

Puzzle #TypeIndexAnirbidChandranathKoushikSuranjan
1V4425
2N9647
3N1110712
4V14131218
5N19171421
6N22211623
7N27231926
8V29262528
9V33282930
10N37303135

 

Step 3 – Assign V and N indices (Index column)

Clue used: We now know the order of all Visual and Number puzzles:

  • Types in order: V, N, N, V, N, N, N, V, V, N

We walk from Puzzle 1 to 10 and count:

  • Puzzle 1: first Visual → V1
  • Puzzle 2: first Number → N1
  • Puzzle 3: second Number → N2
  • Puzzle 4: second Visual → V2
  • Puzzle 5: third Number → N3
  • Puzzle 6: fourth Number → N4
  • Puzzle 7: fifth Number → N5
  • Puzzle 8: third Visual → V3
  • Puzzle 9: fourth Visual → V4
  • Puzzle 10: sixth Number → N6

Now fill the Index column:

Puzzle #TypeIndexAnirbidChandranathKoushikSuranjan
1VV14425
2NN19647
3NN21110712
4VV214131218
5NN319171421
6NN422211623
7NN527231926
8VV329262528
9VV433282930
10NN637303135

Which of the following is the closest to the average time taken by Anirbid to solve the number-based puzzles in the competition?

1. 3.3 minutes

2. 3.8 minutes

3. 2.5 minutes

4. 4.0 minutes

Answer & Explanation

Correct Answer: 4.0 minutes

Explanation: Anirbid’s number-based puzzles are puzzles 2, 3, 5, 6, 7, and 10. The time taken for each is found by subtracting the completion time of the previous puzzle from the completion time of the current puzzle. Puzzle 2 takes 5 minutes, puzzle 3 takes 2 minutes, puzzle 5 takes 5 minutes, puzzle 6 takes 3 minutes, puzzle 7 takes 5 minutes, and puzzle 10 takes 4 minutes. The total time spent on number-based puzzles is 24 minutes across 6 puzzles. Dividing 24 by 6 gives an average of exactly 4.0 minutes.

The graphs converted to table for ease of understanding

Final Puzzle Completion Time Table (Time in Minutes)

Puzzles SolvedAnirbid (Red)Chandranath (Yellow)Koushik (Green)Suranjan (Blue)
14425
29647
31110712
414131218
519171421
622211623
727231926
829262528
933282930
1037303135

Visual Puzzles Completion Times (Time in Minutes)

Order of CompletionAnirbidChandranathKoushikSuranjan
1st Visual Puzzle4425
2nd Visual Puzzle14131218
3rd Visual Puzzle29262528
4th Visual Puzzle33282930

Step 0 – Start with a blank skeleton

Clue used: We know there are 10 puzzles and 4 competitors, and we ultimately want: Puzzle #, Type (V/N), Index (V1, N3, etc.), and completion times.

Blank structure:

Puzzle #TypeIndexAnirbidChandranathKoushikSuranjan
1
2
3
4
5
6
7
8
9
10

 

Step 1 – Fill completion times from “Total Puzzles Solved” table

Clue used:
The “Final Puzzle Completion Time” table gives, for each competitor, the time when each puzzle was completed.

We just copy those times row-wise.

Puzzle #TypeIndexAnirbidChandranathKoushikSuranjan
14425
29647
31110712
414131218
519171421
622211623
727231926
829262528
933282930
1037303135

No calculations yet, just transcription.

Step 2 – Identify which puzzle numbers are Visual (using Koushik)

Clue used:
From the Visual Puzzles Completion Times for Koushik:

  • 1st visual at 2 min
  • 2nd visual at 12 min
  • 3rd visual at 25 min
  • 4th visual at 29 min

Compare these with Koushik’s total completion times:

  • Puzzle 1 = 2 min → matches 1st visual → Puzzle 1 is Visual (V).
  • Puzzle 4 = 12 min → matches 2nd visual → Puzzle 4 is V.
  • Puzzle 8 = 25 min → matches 3rd visual → Puzzle 8 is V.
  • Puzzle 9 = 29 min → matches 4th visual → Puzzle 9 is V.

Fill Type = V in those rows; others will be N.

Puzzle #TypeIndexAnirbidChandranathKoushikSuranjan
1V4425
2N9647
3N1110712
4V14131218
5N19171421
6N22211623
7N27231926
8V29262528
9V33282930
10N37303135

 

Step 3 – Assign V and N indices (Index column)

Clue used: We now know the order of all Visual and Number puzzles:

  • Types in order: V, N, N, V, N, N, N, V, V, N

We walk from Puzzle 1 to 10 and count:

  • Puzzle 1: first Visual → V1
  • Puzzle 2: first Number → N1
  • Puzzle 3: second Number → N2
  • Puzzle 4: second Visual → V2
  • Puzzle 5: third Number → N3
  • Puzzle 6: fourth Number → N4
  • Puzzle 7: fifth Number → N5
  • Puzzle 8: third Visual → V3
  • Puzzle 9: fourth Visual → V4
  • Puzzle 10: sixth Number → N6

Now fill the Index column:

Puzzle #TypeIndexAnirbidChandranathKoushikSuranjan
1VV14425
2NN19647
3NN21110712
4VV214131218
5NN319171421
6NN422211623
7NN527231926
8VV329262528
9VV433282930
10NN637303135

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