Build A Neighborhood Park Without Destroying The Neighborhood

Computer Science Level 3

Josie is planning out a new community park in a suburban neighborhood. The community agrees that the park (which must be rectangular) should be as big as possible, but there are several homeowners who refuse to surrender their properties to the new development.

If the following grid shows (in black) the homeowners who are not willing to sell, what is the largest possible size for the park (in lots)?

The answer is 84.

7 solutions

Finn Hulse
Jan 29, 2014

Okay... I just solved this but I forgot which rectangle I found... But pretty much you look for large gaps and then do some counting... Or you could write an immensely complex computer program... But I like my solution. But how is it that as soon as he had posted this problem, it was assigned a rating? How come I can't do that with my problems? Wahh... How do I do the same?

Probably, next step in these set of problems is this: "If you are allowed to forcefully evict one person from the grid so that you get the maximum area, who will that be?"

Arun Vijayan - 7 years, 4 months ago

The rectangle is at the bottom and has a width of $28$ and a height of $3$ . $28 \times 3 = \boxed{84}$

Arman Siddique - 7 years, 4 months ago

Actually, on my first try, I answered $81$ because I counted $27$ for the width, and on my second try, I answered $87$ because I counted $29$ for the width :/

Arman Siddique - 7 years, 4 months ago

On my first try, I answered $28\cdot3=84$ because I can count. :-/ (Hmm Arman, I guessed you never learned to count since the Algebra II midterm where you got a B because you counted wrong.)

William Cui - 7 years, 4 months ago

Finn, we will be making this feature available to more people once we are satisfied with it.

Suyeon Khim Staff - 7 years, 4 months ago

Hello! That's the first time you've ever replied to me! :D

Finn Hulse - 7 years, 1 month ago

Image files are extremely hard to parse,hence the lack of CS solutions..It would have been great if the grid had been provided in a text file or something.

Thaddeus Abiy - 7 years, 4 months ago