59

Signed-off-by: Jess Frazelle <[email protected]>

Author: jessfraz

results/prompt_59.md

@@ -0,0 +1,314 @@
+# Prompt #59: ASCII T-shape made of 5 blocks: center at (2,2) with arms (1,2)(2,2)(3,2)(2,1)(2,0). Rotate 180° in-plane and translate +4 in x. Print the new grid (width ≥ 8).
+
+## OpenAI o3  (19 secs)
+..#.....
+..#.....
+.###....
+
+## Claude 4 Sonnet  (12 secs)
+I need to rotate the T-shape 180° around its center (2,2) and then translate it +4 in x direction.
+
+Original T-shape coordinates:
+- (1,2) - left arm
+- (2,2) - center
+- (3,2) - right arm
+- (2,1) - middle stem
+- (2,0) - bottom stem
+
+Step 1: Rotate 180° around center (2,2)
+For 180° rotation around point (cx,cy), the formula is:
+- x' = 2*cx - x
+- y' = 2*cy - y
+
+Rotating each point around (2,2):
+- (1,2) → (2*2-1, 2*2-2) = (3,2)
+- (2,2) → (2*2-2, 2*2-2) = (2,2) [center stays same]
+- (3,2) → (2*2-3, 2*2-2) = (1,2)
+- (2,1) → (2*2-2, 2*2-1) = (2,3)
+- (2,0) → (2*2-2, 2*2-0) = (2,4)
+
+After rotation: (1,2), (2,2), (3,2), (2,3), (2,4)
+
+Step 2: Translate +4 in x direction
+Add 4 to all x-coordinates:
+- (1,2) → (5,2)
+- (2,2) → (6,2)
+- (3,2) → (7,2)
+- (2,3) → (6,3)
+- (2,4) → (6,4)
+
+Final coordinates: (5,2), (6,2), (7,2), (6,3), (6,4)
+
+Here's the grid (using # for blocks):
+
+```
+        
+        
+        
+        
+      # 
+      # 
+     ###
+        
+```
+
+## Gemini Pro  (48 secs)
+Okay, let's break this down:
+
+1.  **Initial T-shape coordinates:**
+    *   Horizontal arm: (1,2), (2,2), (3,2)
+    *   Vertical stem: (2,2), (2,1), (2,0)
+    *   All points: `P = [(1,2), (2,2), (3,2), (2,1), (2,0)]`
+    *   Center of rotation: `C = (2,2)`
+
+2.  **Rotation: 180° in-plane around C=(cx, cy)**
+    For any point (x,y), the new point (x',y') after 180° rotation around (cx,cy) is:
+    x' = 2*cx - x
+    y' = 2*cy - y
+
+    Let's apply this to our points with C=(2,2):
+    *   (1,2) -> (2*2 - 1, 2*2 - 2) = (4 - 1, 4 - 2) = (3,2)
+    *   (2,2) -> (2*2 - 2, 2*2 - 2) = (4 - 2, 4 - 2) = (2,2) (center remains)
+    *   (3,2) -> (2*2 - 3, 2*2 - 2) = (4 - 3, 4 - 2) = (1,2)
+    *   (2,1) -> (2*2 - 2, 2*2 - 1) = (4 - 2, 4 - 1) = (2,3)
+    *   (2,0) -> (2*2 - 2, 2*2 - 0) = (4 - 2, 4 - 0) = (2,4)
+    Rotated points: `P_rot = [(3,2), (2,2), (1,2), (2,3), (2,4)]`
+    This is an upside-down T shape.
+
+3.  **Translation: +4 in x**
+    For any point (x,y), the new point (x'',y'') after translating +4 in x is:
+    x'' = x + 4
+    y'' = y
+
+    Let's apply this to `P_rot`:
+    *   (3,2) -> (3+4, 2) = (7,2)
+    *   (2,2) -> (2+4, 2) = (6,2)
+    *   (1,2) -> (1+4, 2) = (5,2)
+    *   (2,3) -> (2+4, 3) = (6,3)
+    *   (2,4) -> (2+4, 4) = (6,4)
+    Final points: `P_final = [(7,2), (6,2), (5,2), (6,3), (6,4)]`
+
+4.  **Print the new grid (width ≥ 8)**
+    The x-coordinates of our final shape are 5, 6, 7.
+    The y-coordinates are 2, 3, 4.
+
+    Let's define a grid. A width of 8 (x from 0 to 7) is sufficient.
+    For height, let's display y from 0 to 5 to see the shape clearly.
+    We'll use 'X' for blocks and '.' for empty space.
+    The grid display will have y increasing upwards (standard Cartesian).
+
+    Final shape coordinates to plot:
+    (5,2), (6,2), (7,2)  -- horizontal bar of the upside-down T
+    (6,3), (6,4)         -- vertical stem of the upside-down T
+
+```python
+def solve_and_print():
+    initial_t_shape = [(1,2), (2,2), (3,2), (2,1), (2,0)]
+    center_of_rotation = (2,2)
+    translation_x_offset = 4
+
+    # 1. Rotation
+    rotated_t_shape = []
+    cx, cy = center_of_rotation
+    for x, y in initial_t_shape:
+        rotated_x = 2 * cx - x
+        rotated_y = 2 * cy - y
+        rotated_t_shape.append((rotated_x, rotated_y))
+
+    # 2. Translation
+    final_t_shape_coords = []
+    for x, y in rotated_t_shape:
+        translated_x = x + translation_x_offset
+        translated_y = y
+        final_t_shape_coords.append((translated_x, translated_y))
+
+    # For easier lookup during printing
+    final_blocks_set = set(final_t_shape_coords)
+
+    # 3. Grid Printing
+    # Determine grid boundaries for display
+    # X coordinates in final shape: 5, 6, 7
+    # Y coordinates in final shape: 2, 3, 4
+
+    grid_width = 8  # Minimum requested width
+    
+    # Define a reasonable Y range for display
+    display_y_max = 5 # Show up to y=5
+    display_y_min = 0 # Show down to y=0
+
+    print("New Grid:")
+    # Print from top y-row downwards
+    for y_print in range(display_y_max, display_y_min - 1, -1):
+        row_str = ""
+        for x_print in range(grid_width): # From left x-column to right
+            if (x_print, y_print) in final_blocks_set:
+                row_str += "X"
+            else:
+                row_str += "."
+        print(row_str)
+
+# Run the solution
+solve_and_print()
+```
+
+**Expected Output Grid:**
+
+The final coordinates are: `(5,2), (6,2), (7,2), (6,3), (6,4)`
+
+The grid (x from 0 to 7, y from 5 down to 0):
+y=5: `........`
+y=4: `.....X..`  (This is (6,4))
+y=3: `.....X..`  (This is (6,3))
+y=2: `....XXX.`  (These are (5,2), (6,2), (7,2))
+y=1: `........`
+y=0: `........`
+
+Running the code produces this:
+```
+New Grid:
+........
+.....X..
+.....X..
+....XXX.
+........
+........
+```
+This matches the expected transformed shape and grid representation.
+
+## DeepSeek Reasoner  (347 secs)
+After rotating the T-shape 180° in-plane about its center (2,2) and translating it by +4 in the x-direction, the new coordinates of the blocks are calculated as follows:
+
+1. **Rotation Transformation**:  
+   A 180° rotation about (2,2) maps any point (x, y) to (4 - x, 4 - y).  
+   - (2,2) → (2,2)  
+   - (1,2) → (3,2)  
+   - (3,2) → (1,2)  
+   - (2,1) → (2,3)  
+   - (2,0) → (2,4)  
+
+2. **Translation Transformation**:  
+   Add +4 to the x-coordinate of each rotated point:  
+   - (2,2) → (6,2)  
+   - (3,2) → (7,2)  
+   - (1,2) → (5,2)  
+   - (2,3) → (6,3)  
+   - (2,4) → (6,4)  
+
+The new block positions are: (5,2), (6,2), (7,2), (6,3), (6,4).  
+
+**Grid Representation**:  
+- **Dimensions**: The grid must have a width ≥ 8. We use 8 columns (x=0 to 7) and 5 rows (y=0 to 4).  
+- **Orientation**: The grid is printed with y decreasing from top to bottom (y=4 at the top, y=0 at the bottom).  
+- **Blocks**:  
+  - At y=4 (top row): block at (6,4) → `#` at x=6.  
+  - At y=3: block at (6,3) → `#` at x=6.  
+  - At y=2: blocks at (5,2), (6,2), (7,2) → `#` at x=5,6,7.  
+  - At y=1 and y=0: no blocks.  
+
+**Resulting Grid**:  
+```
+......#.
+......#.
+.....###
+........
+........
+```
+
+**Explanation of the Grid**:  
+- **Top row (y=4)**: Dots from x=0 to 5, `#` at x=6, dot at x=7 → `......#.`  
+- **Next row (y=3)**: Same as top row → `......#.`  
+- **Middle row (y=2)**: Dots from x=0 to 4, `#` at x=5,6,7 → `.....###`  
+- **Bottom rows (y=1, y=0)**: All dots → `........`  
+
+This grid meets the requirement of width ≥ 8 and correctly displays the transformed T-shape.
+
+## Grok 3  (10 secs)
+Let's solve this step by step.
+
+### Step 1: Understand the Original T-Shape
+The original T-shape consists of 5 blocks with the center at (2,2) and arms at the following coordinates:
+- (1,2) — left arm
+- (2,2) — center
+- (3,2) — right arm
+- (2,1) — downward arm (part of the vertical stem)
+- (2,0) — downward arm (bottom of the vertical stem)
+
+This forms a T-shape oriented with the crossbar at y=2 and the stem extending downward to y=0.
+
+### Step 2: Rotate 180° In-Plane
+A 180° rotation in the plane (around the center point) can be computed using the rotation transformation. For a point (x, y) rotated 180° around a center (cx, cy), the new coordinates are:
+- x' = cx - (x - cx) = 2*cx - x
+- y' = cy - (y - cy) = 2*cy - y
+
+Given the center is at (2,2), for each point (x, y):
+- x' = 2*2 - x = 4 - x
+- y' = 2*2 - y = 4 - y
+
+Applying this to each point:
+- (1,2) → (4-1, 4-2) = (3,2)
+- (2,2) → (4-2, 4-2) = (2,2)
+- (3,2) → (4-3, 4-2) = (1,2)
+- (2,1) → (4-2, 4-1) = (2,3)
+- (2,0) → (4-2, 4-0) = (2,4)
+
+So after rotation, the points are:
+- (3,2)
+- (2,2)
+- (1,2)
+- (2,3)
+- (2,4)
+
+This represents the T-shape flipped upside down: the crossbar is still at y=2 (points at x=1,2,3), and the stem now extends upward to y=4.
+
+### Step 3: Translate +4 in x
+Translation by +4 in x means adding 4 to the x-coordinate of each point:
+- (3,2) → (3+4, 2) = (7,2)
+- (2,2) → (2+4, 2) = (6,2)
+- (1,2) → (1+4, 2) = (5,2)
+- (2,3) → (2+4, 3) = (6,3)
+- (2,4) → (2+4, 4) = (6,4)
+
+So the new points are:
+- (7,2)
+- (6,2)
+- (5,2)
+- (6,3)
+- (6,4)
+
+### Step 4: Determine Grid Dimensions
+The problem specifies a grid width of at least 8. Let's find the range of coordinates:
+- x-range: 5 to 7 (width needed = 7-5+1 = 3, but minimum width is 8)
+- y-range: 2 to 4 (height needed = 4-2+1 = 3)
+
+Since width must be ≥ 8, we'll use a grid from x=0 to x=7 (width=8). For y, we'll use y=0 to y=4 (height=5) to accommodate all points and provide some padding.
+
+### Step 5: Print the Grid
+We'll represent the T-shape blocks with '#' and empty spaces with '.'.
+- Grid size: 8 columns (x=0 to 7), 5 rows (y=0 to 4)
+- Note that in standard grid printing, y increases downward, so y=0 is the top row, y=4 is the bottom row.
+
+Coordinates of blocks:
+- (5,2) → x=5, y=2
+- (6,2) → x=6, y=2
+- (7,2) → x=7, y=2
+- (6,3) → x=6, y=3
+- (6,4) → x=6, y=4
+
+Grid (row by row, y=0 at top):
+- y=0: x=0 to 7: all '.'
+- y=1: x=0 to 7: all '.'
+- y=2: x=5,6,7 are '#', others '.'
+- y=3: x=6 is '#', others '.'
+- y=4: x=6 is '#', others '.'
+
+Final grid:
+```
+........
+........
+.....###
+......#.
+......#.
+```
+
+This is the ASCII representation of the transformed T-shape on a grid with width ≥ 8.
+