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.

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

The correct answer is 2.

To find the time Suranjan took to solve the third visual puzzle, we can analyze the sequence of puzzles solved using the two charts provided: "All puzzles" (on the left) and "Visual puzzles" (on the right).

1. Understanding the Chart Grid:
On both charts, the horizontal axis (Time) has major solid grid lines at intervals of 10 minutes (0, 10, 20, 30, 40). Between any two major solid lines, there are 4 dashed grid lines, which divide each 10-minute interval into 5 equal parts. Therefore, each grid line represents:

$\frac{10\text{minutes}}{5}=2\text{minutes}$

2. Identifying the Puzzle Sequence:
Since all competitors solve the puzzles in the exact same sequence, the puzzle types (visual or number-based) are identical for everyone. Let's trace Koushik's (green line) progress to classify the puzzles:
• Puzzle 1: Koushik solves his first puzzle at 2 minutes. His visual puzzles count jumps from 0 to 1 at 2 minutes. This means Puzzle 1 is a visual puzzle (Visual Puzzle #1).
• Puzzles 2 & 3: Koushik solves his 2nd and 3rd puzzles at 4 minutes and 7 minutes, respectively, but his visual puzzle count remains at 1. This means Puzzles 2 and 3 are number-based.
• Puzzle 4: Koushik solves his 4th puzzle at 12 minutes, and his visual puzzle count jumps from 1 to 2. This means Puzzle 4 is a visual puzzle (Visual Puzzle #2).
• Puzzles 5, 6, & 7: Koushik solves his 5th, 6th, and 7th puzzles at 14, 16, and 19 minutes, respectively, while his visual puzzle count remains at 2.
• Puzzle 8: Koushik solves his 8th puzzle at 24 minutes, and his visual puzzle count jumps from 2 to 3. This means Puzzle 8 is a visual puzzle (Visual Puzzle #3).

3. Tracking Suranjan's Progress for the Third Visual Puzzle (Puzzle 8):
Now we look at Suranjan's progress (represented by the light blue/cyan line) on the "All puzzles" chart to find the start and end times for Puzzle 8:
• Suranjan solves his 7th puzzle (Puzzle 7) at exactly 28 minutes (the fourth dashed line after 20). This is when he gets access to Puzzle 8.
• Suranjan solves his 8th puzzle (Puzzle 8, which is the 3rd visual puzzle) at exactly 30 minutes (the solid line for 30).

4. Calculating the Time Taken:
The time Suranjan spent solving the 3rd visual puzzle is the difference between the completion time of Puzzle 8 and Puzzle 7:

$30-28=2\text{minutes}$