Question
Which of the following figures can be drawn without lifting the pen from the paper or retracing? 
The correct answer is
figure A but not figure B
To determine whether a figure can be drawn without lifting the pen from the paper or retracing any line, we look at the concept of Eulerian paths in graph theory. A figure can be drawn in such a manner if it has exactly zero or two vertices of odd degree. Let's analyze both figures based on this principle.
- Analyzing Figure A:
- Identify the vertices: Figure A has four vertices.
- Degree of vertices: Upon inspection, it is seen that all four vertices have an even degree.
- Conclusion: Since all vertices have even degrees, Figure A can be drawn without lifting the pen or retracing.
- Analyzing Figure B:
- Identify the vertices: Figure B has five vertices.
- Degree of vertices: We find three vertices have an odd degree.
- Conclusion: Since more than two vertices have an odd degree, Figure B cannot be drawn without lifting the pen or retracing.
Correct Answer: Figure A but not Figure B
In conclusion, based on Eulerian path theory, only Figure A can be drawn without lifting the pen from the paper or retracing any lines.
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Important Questions from Puzzle (Notes)
- Four individuals - P, Q, R and S - are suspects in a theft case. They make the following statements :
P says: "Q is guilty."
Q says: "R is guilty."
R says: "P is innocent."
S says: "I am innocent"
If it is known that exactly one of them is guilty, and only the guilty person lies (all innocent people tell the truth), then who is the guilty one? - In which company, C's interview was scheduled?
- Who went to Nagpur?
- What is the sum of the digits of the number Q?
- What is the sum of A and Q if A is smaller than B?
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