This a probability problem. you have 16 cells out of which u need to take out 5 cells that are somehow connected. So find the total number of cases then eliminate those you don't need such as the corner cells. or you can simply count the cases...
I wasn't entirely sure where to post this so I guessed here would be the best place.
See the figure attached for the problem statement.
How do you go about solving a problem like this? There must some sort of proof to go along with it explaining how this undoubtedly the maximum number of 5 cell figures, right?
I'm not doing a math degree or anything so maybe this is a common type of problem in a certain area of mathematics.
Can somebody help clear things up? A start at the problem would be nice!
Maybe these will help you
Polyomino - Wikipedia, the free encyclopedia
Pentomino - Wikipedia, the free encyclopedia
Those are called polyominoes. You are certainly familiar with dominoes (d - two, omino), well, the ones in your problem involves pentominoes (pent - five, omino)
If you want to try something else (kinda similar), go here:
Problem #19
Alternate way to place 8 figures, of course the figures can be shifted to get some more arrangements.
Edit: sorry the image is so big, i don't have photoshop on this computer and it's a bit of a hassle to resize in a way that looks nice.