PartialMathematician

\(18= 3/4 (2w-1)\)

I would directly multiply both sides by \(\dfrac{4}{3}\) to get \(24 = 2w-1\). Adding 1 to both sides, we have \(2w = 25\), and by dividing both sides by 2, we have \(\boxed{12.5}\) or \(\boxed{12\dfrac{1}{2}}\).

- PM

Except I am not quite sure what that means...

According to Google, OCA is Orthodox Church in America.

In 5! and up, there is a 2 and a 5, and when multiplied, they equal 10, which has a 0 in the units digit.

Case 1: We choose two points that are on the same side of the square. There are 38 other points, 8 of which are on the same side. There are 30 points to choose from so that they are not collinear. 

Case 2: We choose two points that are not on the same side. At this point, any of the other 38 points work.

We also need to consider the 4 vertices, so we subtract our total possible centroids by 4. 

30 + 38 -4 = 64, so there are \(64\) possible centroids. 

I am not 100% sure about my answer though.

We have 5 options and must choose 4. However, the same color can be used more than once. 5*4 = 20, and  \({20}\choose{4}\) = 4845.

We did overcount (Example: 1234 is the same as 2341, but we counted it twice), so to take away overcounting, we divide 4845 by 5 to get 969. With some other casework and steps shown below, you will end up with \(\boxed{165}\).

Do not try to list out the answers because there are many and that is inefficient. Always use number theory. 

- PM

Math is required for many jobs, such as engineering, doctors, even contractors.