Editing Openai/6933ffb6-9ed8-8010-99bb-a5bc968f2d9b (section)

=== User: I think Gemini might have beat you on your own game. ===
I think Gemini might have beat you on your own game. Look at prompt 3, where Gemini actually seems to have find a shortest path for answer:

"Find the smallest positive integer 
n
n such that:
n
≡
7
(
m
o
d
11
)
n≡7(mod11)
n
≡
4
(
m
o
d
13
)
n≡4(mod13)
n
≡
10
(
m
o
d
17
)
n≡10(mod17)
Provide the exact integer.

Based on the grid provided in the image, here is the step-by-step solution:

Grid Analysis (1-based indexing):

Row 2: #S..#.# 
→
→
 Start is at (2,2). There is a path to the right: (2,3) and (2,4). (2,5) is a wall.
Row 3-5: Center column (Column 4) is open (.) in all these rows, while Column 3 is a wall (#).
Row 6: #.#...# 
→
→
 Column 4 is open.
Row 7: ###E### 
→
→
 End is at (7,4). The only way to access E is from directly above it at (6,4), as (7,3) and (7,5) are walls.
Pathfinding:
The only route from the Start (2,2) to the vertical corridor in Column 4 is to move right along Row 2. Once in Column 4, you can move straight down to the End.

Start at (2,2)
Move Right to (2,3)
Move Right to (2,4)
Move Down to (3,4)
Move Down to (4,4)
Move Down to (5,4)
Move Down to (6,4)
Move Down to (7,4) [End]
Answers:
# Is there ANY valid path from S to E?
Yes
# Exact length of the shortest path:
7 steps
# Valid shortest path sequence:
(2,2), (2,3), (2,4), (3,4), (4,4), (5,4), (6,4), (7,4)"