Critical Thinking Worksheets - 15 Worksheets Library - Free Printable

Problem Analysis:

The task involves solving four puzzles by removing specific lines to achieve certain geometric configurations. Each puzzle requires critical thinking and spatial reasoning to determine which lines to remove.

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Puzzle 1: Remove 4 bars to make two equal shapes.

#### Solution:
- The goal is to remove 4 bars such that the remaining structure forms two equal shapes.
- Observing the grid, we can see that it consists of a larger square with some internal lines.
- By removing the following 4 bars:
- The horizontal bar in the middle row (connecting the second and third columns).
- The vertical bar in the middle column (connecting the second and third rows).
- The horizontal bar at the top (connecting the first and second columns).
- The horizontal bar at the bottom (connecting the first and second columns).

This will split the grid into two identical L-shaped figures.

#### Explanation:
By removing these 4 bars, the grid is divided into two symmetrical L-shapes, each consisting of 5 squares.

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Puzzle 2: Remove 5 bars to make 6 squares.

#### Solution:
- The goal is to remove 5 bars such that the remaining structure forms exactly 6 squares.
- The grid currently has 9 squares (a 3x3 grid). To reduce it to 6 squares, we need to "merge" some squares by removing specific bars.
- By removing the following 5 bars:
- The horizontal bar in the middle row (connecting all columns).
- The vertical bar in the middle column (connecting all rows).
- The horizontal bar at the top (connecting the first and second columns).
- The horizontal bar at the bottom (connecting the first and second columns).
- The vertical bar on the far right (connecting the top and bottom rows).

This will leave us with 6 squares: one large square in the center and five smaller squares around it.

#### Explanation:
By removing these 5 bars, the grid is reconfigured to form 6 distinct squares.

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Puzzle 3: Remove 6 bars to make 2 rectangles and 2 squares.

#### Solution:
- The goal is to remove 6 bars such that the remaining structure forms 2 rectangles and 2 squares.
- The grid currently has 9 squares (a 3x3 grid). To achieve the desired configuration, we need to merge some squares into rectangles while keeping others as squares.
- By removing the following 6 bars:
- The horizontal bar in the middle row (connecting all columns).
- The vertical bar in the middle column (connecting all rows).
- The horizontal bar at the top (connecting the first and second columns).
- The horizontal bar at the bottom (connecting the first and second columns).
- The vertical bar on the far left (connecting the top and bottom rows).
- The vertical bar on the far right (connecting the top and bottom rows).

This will leave us with:
- Two rectangles (formed by the outer edges of the grid).
- Two squares (formed in the corners of the grid).

#### Explanation:
By removing these 6 bars, the grid is reconfigured to form 2 rectangles and 2 squares.

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Puzzle 4: Remove 11 bars to make 4 squares.

#### Solution:
- The goal is to remove 11 bars such that the remaining structure forms exactly 4 squares.
- The grid currently has 9 squares (a 3x3 grid). To reduce it to 4 squares, we need to "merge" most of the squares by removing specific bars.
- By removing the following 11 bars:
- All horizontal bars except the middle one.
- All vertical bars except the middle one.

This will leave us with 4 squares: one large square in the center and three smaller squares around it.

#### Explanation:
By removing these 11 bars, the grid is reconfigured to form 4 distinct squares.

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Final Answer:

\[
\boxed{
\text{
1. Remove the middle horizontal bar, middle vertical bar, top horizontal bar, and bottom horizontal bar.
2. Remove the middle horizontal bar, middle vertical bar, top horizontal bar, bottom horizontal bar, far-left vertical bar, and far-right vertical bar.
3. Remove the middle horizontal bar, middle vertical bar, top horizontal bar, bottom horizontal bar, far-left vertical bar, and far-right vertical bar.
4. Remove all horizontal bars except the middle one, and all vertical bars except the middle one.
}}
\]