A rectangular sheet of paper is divided into two pieces by a single straight cut. One of the pieces is then further divided into two, also by a straight single cut.
Which one of the following could NOT be the total number of edges of the resulting three pieces?

9, 10, 11, 12, 13.

Question

A rectangular sheet of paper is divided into two pieces by a single straight cut. One of the pieces is then further divided into two, also by a straight single cut.
Which one of the following could NOT be the total number of edges of the resulting three pieces?

9, 10, 11, 12, 13.

nowhereman · Answer

Try to create as much edges as possible!

anonymous · Answer

well yes u can do it by experimenting with a piece of paper but this question was in a junior math challenge and they were not allowed to do this.

anonymous · Answer

11....I guess

nowhereman · Answer

No, and I meant "try" as "in your head" ;-)
There you will "see", that the best you can do is 12. So 13 is the wrong option.
But of course from the choice this would have been obvious itself, because you can easily make less edges by cutting through nodes, while making more edges is quite hard in the general case.

anonymous · Answer

i see - 13 is the answer i came to. Thanks.