Am I logical?

Logic Level 3

You have 10 trees in a plane. Arrange them in such a manner that there exists 5 lines which contain exactly 4 trees.

If we connect up these rows of 4 trees with line segments, how many distinct bounded regions are there in the plane?

The answer is 6.

1 solution

Abhinav Jha
May 9, 2016

a star shape.

Is this logical? Is this the only possible solution (up to equivalence)? Why can't there be another way to arrange these trees?

Calvin Lin Staff - 5 years, 1 month ago

See the forest through the trees

Very similar question, so free points! :P

Sharky Kesa - 5 years, 1 month ago

I have arrived to the solution in which central figure is a Triangle .... Is it the maximum number of lines which contains four trees each??

Adarsh Adi - 3 years, 3 months ago

I thought the outside is also included hahaha

Rindell Mabunga - 5 years, 1 month ago

Those who answered 7 have been marked correct. I have edited the problem for clarity.

In future, if you spot any errors with a problem, you can “report” it by selecting "report problem" in the menu. This will notify the problem creator who can fix the issues.

Calvin Lin Staff - 5 years, 1 month ago

I had asked for 'how many POLYGONS are there' and polygons are closed. There is no need to include out side region. By the way thanks for editing the problem now its more clearer.

Abhinav Jha - 5 years, 1 month ago

@Abhinav Jha – Because the phrasing of "the number of polygon (with no common area) that divide the plane" is extremely ambiguous (e.g we could just have 1 star polygon), hence I had replaced it with "distinct regions in the plane"

Calvin Lin Staff - 5 years, 1 month ago

@Calvin Lin – Oh true. Thanks again.

Abhinav Jha - 5 years, 1 month ago

Am I logical?

The answer is 6.

1 solution

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