Instructions [34 - 37 ]

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.

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

The correct answer is 6.

Step-by-Step Analysis:

1. Understanding the Charts:
The chart on the left ("All puzzles") displays the cumulative number of puzzles (both visual and number-based) solved by each of the four participants over time.
The chart on the right ("Visual puzzles") displays the cumulative number of visual puzzles solved by each participant over time.
Since all competitors solve the 10 puzzles in the exact same sequence, we can determine whether a puzzle at a given position in the sequence is a visual puzzle or a number-based puzzle by matching the completion times of the puzzles on both charts for any participant.

2. Identifying the Visual Puzzles:
Let us trace the puzzle completion times for Koushik (green line):
• 1st Puzzle: Solved at $t=2$ minutes (both total and visual counts increase at $t=2$). Hence, Puzzle 1 is Visual.
• 2nd Puzzle: Solved at $t=4$ minutes.
• 3rd Puzzle: Solved at $t=7$ minutes.
• 4th Puzzle: Solved at $t=12$ minutes. The visual count increases to 2 at $t=12$. Hence, Puzzle 4 is Visual.
• 5th Puzzle: Solved at $t=14$ minutes.
• 6th Puzzle: Solved at $t=16$ minutes.
• 7th Puzzle: Solved at $t=19$ minutes.
• 8th Puzzle: Solved at $t=25$ minutes. The visual count increases to 3 at $t=25$. Hence, Puzzle 8 is Visual.
• 9th Puzzle: Solved at $t=28$ minutes. The visual count increases to 4 at $t=28$. Hence, Puzzle 9 is Visual.
• 10th Puzzle: Solved at $t=30$ minutes. The total visual puzzles solved remains 4 at the end of the competition.

3. Classification of Puzzles:
From the analysis above, we establish the nature of each of the 10 puzzles in sequence:
• Puzzle 1: Visual
• Puzzle 2: Number-based (1st number-based puzzle)
• Puzzle 3: Number-based (2nd number-based puzzle)
• Puzzle 4: Visual
• Puzzle 5: Number-based (3rd number-based puzzle)
• Puzzle 6: Number-based (4th number-based puzzle)
• Puzzle 7: Number-based (5th number-based puzzle)
• Puzzle 8: Visual
• Puzzle 9: Visual
• Puzzle 10: Number-based (6th number-based puzzle)

Thus, the 4th number-based puzzle is at sequence number 6.