Which of the following figures can be drawn without lifting the pen from the paper or retracing? 
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.
Important Questions from Puzzle (Notes)
- Seven boxes S, F, G, H, T and U are kept one over the other but not necessarily in the same order. Only two boxes are kept below S. Only one box is kept above U. Only one box is kept between U and B. G is kept immediately above F. T is kept at some place below H.
How many boxes are kept between H and G? - Seven boxes E, F, G, H, S, T and U are kept one over the other but not necessarily in the same order. H is kept immediately above E. T is kept immediately above U. Only F is kept above S. Only two boxes are kept above H. T is not kept at third position from the bottom.
How many boxes are kept between G and F? - Seven boxes E, F, G, H, S, T and U are kept one over the other but not necessarily in the same order. Only H is kept above E. Only T is kept between E and S. Only F is kept below U.
How many boxes are kept between G and F? Seven boxes E, F, G, H, S, T and U are kept one over the other but not necessarily in the same order. Only four boxes are kept between H and E. Only S is kept above H. Only two boxes are kept between F and U. T is kept immediately above G. U is not kept immediately above T. Which box is kept fourth from the top?
- Seven boxes E, F, G, H, S, T and U are kept one over the other but not necessarily in the same order. Only H is kept above E. Only T is kept between E and S. Only F is kept below U.
How many boxes are kept between G and F?
