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:
Let us determine the types of all the 10 puzzles (whether they are visual or number-based) by analyzing the two charts provided:
1. The left chart ("All puzzles") tracks the total number of puzzles solved by each competitor over time.
2. The right chart ("Visual puzzles") tracks only the number of visual puzzles solved by each competitor over time.

By comparing the times at which the total number of solved puzzles increases with the times at which the visual puzzle count increases, we can identify which specific puzzles in the sequence are visual puzzles.

Let us analyze the progress of one competitor, Koushik (represented by the green line):
- Koushik solves Puzzle 1 at $t=2$ minutes (his total solved count goes from 0 to 1). At this exact time ($t=2$ minutes), his visual puzzles solved count also increases from 0 to 1. This means Puzzle 1 is a visual puzzle.
- Koushik solves Puzzle 4 at $t=12$ minutes (his total solved count goes from 3 to 4). At this exact time ($t=12$ minutes), his visual puzzles solved count increases from 1 to 2. This means Puzzle 4 is a visual puzzle.
- Koushik solves Puzzle 8 at $t=25$ minutes (his total solved count goes from 7 to 8). At this exact time ($t=25$ minutes), his visual puzzles solved count increases from 2 to 3. This means Puzzle 8 is a visual puzzle.
- Koushik solves Puzzle 9 at $t=28$ minutes (his total solved count goes from 8 to 9). At this exact time ($t=28$ minutes), his visual puzzles solved count increases from 3 to 4. This means Puzzle 9 is a visual puzzle.

We can verify this pattern with another competitor, such as Chandranath (yellow line):
- Chandranath's visual puzzles solved count increases:
   • From 0 to 1 at $t=3$ minutes, which is when he solves Puzzle 1.
   • From 1 to 2 at $t=13$ minutes, which is when he solves Puzzle 4.
   • From 2 to 3 at $t=26$ minutes, which is when he solves Puzzle 8.
   • From 3 to 4 at $t=29$ minutes, which is when he solves Puzzle 9.

Thus, the visual puzzles in the sequence are Puzzles 1, 4, 8, and 9. All other puzzles in the 10-puzzle sequence are number-based.

Let us map out the entire sequence of puzzles from 1 to 10:
- Puzzle 1: Visual (1^st visual)
- Puzzle 2: Number-based (1^st number-based)
- Puzzle 3: Number-based (2^nd number-based)
- Puzzle 4: Visual (2^nd visual)
- Puzzle 5: Number-based (3^rd number-based)
- Puzzle 6: Number-based (4^th number-based)
- Puzzle 7: Number-based (5^th number-based)
- Puzzle 8: Visual (3^rd visual)
- Puzzle 9: Visual (4^th visual)
- Puzzle 10: Number-based (6^th number-based)

From the list above, the fourth number-based puzzle is at position 6 in the sequence.