Is it possible to put 25 Hydroponics basin in the area of one sun lamp?

A sun lamp covers a 100 grids area as following

and a Hydroponics basin requires 4 grids

It's clear that 100 is divisible by 4...

i.e. 100/4=25

However, I tried many ways to put them, it seems the max number is 24 in this case

Is it possible to place 25 Hydroponics basins in the area of one sunlight ?

Thanks for your help.

1 Answer

No, you can only get 24 inside the field. It's easy to show with a coloring argument.

Any Hydroponics Basin placed in this grid must cover exactly one red, one yellow, one blue, and one green square. (Convince yourself that this is true; it's not hard.) However, there are 24 red and blue squares, and 26 yellow and green squares. So not only can you only get 24 basins into the figure, but the four squares you leave empty must be two green and two yellow squares.

This is the same argument that shows you can't get 31 dominoes onto a checkerboard if you cut off two opposite corners; there are different numbers of red and black squares remaining.