The task is to copy the image of a house with a stick figure inside it without lifting your pen from the paper. This type of problem is often related to
Eulerian paths in graph theory, where you must draw a shape by traversing each line exactly once without lifting your pen.
Step-by-Step Solution:
1.
Understand the Problem:
- The goal is to draw the entire image (the house and the stick figure) without lifting your pen.
- This means every line segment must be drawn exactly once.
2.
Analyze the Image:
- The house consists of a triangular roof and a rectangular body with a door.
- The stick figure is inside the door.
3.
Key Insight:
- To solve this, we need to ensure that every point where lines meet (called a vertex) has an even number of lines coming out of it. If there are vertices with an odd number of lines, it becomes impossible to draw the shape without lifting the pen unless we start or end at those points.
4.
Identify Vertices:
- Look at all the corners and intersections in the image:
- The top of the roof has 3 lines meeting (odd).
- The bottom corners of the roof have 3 lines meeting (odd).
- The corners of the house body have 3 lines meeting (odd).
- The door frame has 4 lines meeting (even).
- The stick figure's joints have 2 or 4 lines meeting (even).
5.
Strategy:
- Since there are multiple vertices with an odd number of lines, we cannot draw the entire image in one continuous stroke starting and ending at the same point.
- However, we can still draw the image without lifting the pen if we allow ourselves to start at one odd vertex and end at another odd vertex.
6.
Drawing Sequence:
- Start at one of the odd vertices (e.g., the top of the roof).
- Trace the outline of the roof and then the body of the house, ensuring you pass through each line exactly once.
- When you reach the door, trace the stick figure inside the door, making sure to use the lines of the door as part of the stick figure's limbs.
- Continue until you finish at another odd vertex.
7.
Visualization:
- Imagine drawing the roof first, then moving down to the body of the house.
- Use the door as part of the stick figure's limbs to connect everything seamlessly.
- Ensure no lines are skipped or repeated.
Final Answer:
It is indeed possible to draw the entire image without lifting your pen. The key is to carefully plan the path so that you traverse each line exactly once, starting at one odd vertex and ending at another.
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\boxed{\text{Yes, it is possible to copy the image without lifting your pen.}}
$$
Parent Tip: Review the logic above to help your child master the concept of brain teasers worksheets.
