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Do games always use AI for defining behaviour of opponent players or is it just vector math?

I’m trying to learn how games implement tactics for opponents/enemy player.

In games like Street Fighter with maximum difficult, the opponent (computer) is too good at predicting and countering my moves. Do they use AI (like neural networks) for defining opponent behaviour or can it be achieved using vector math (linear algebra) and collision detection algorithms?

enter image description here

contest math – Olympiad Inequality which can be solved using Cauchy–Schwarz inequality

$x,y,z$ are positive real numbers, such that $x+y+z=3$ . prove that :

$$sum_{mathrm{cyc}}frac{x}{x^3+y^2+z} leq 1 $$

I tried many things , but I don’t think any of those are worth of mentioning.
However, I know problem can be solves using Cauchy–Schwarz inequality.

Please, share your ideas. Thanks.

wikipedia – Why are the characters in the math expressions on some wiki pages slanted or lying down?

When I was looking through some wiki pages, I noticed that some characters were actually slanted or lying down. More precisely, they are reflected horizontally and then rotated 90 degree anticlockwise.

Here are some examples:

Figure 1: https://i.stack.imgur.com/a9BYF.png

From https://en.wikipedia.org/wiki/Nesbitt’s_inequality, at the zooming rate of 150%. If I used other zooming rate, this slanted character will appear normal.

Figure 2: https://i.stack.imgur.com/VwylA.png

From https://en.wikipedia.org/wiki/Nesbitt’s_inequality, under section proof/third proof. In this case, I just used the normal 100% zooming rate.

Figure 3: https://i.stack.imgur.com/Wo0Mi.png

From https://en.wikipedia.org/wiki/Chlorophyll_fluorescence, under Measuring Florescence/ Calculated parameters, with zooming rate of 100%.

For all of these examples, if I just zoomed the screen, these errors will disappear. However, these errors are consistent with the zooming rate stated above, at least on my device.

So, I do not know much about formula editors and curious of this phenomenon. Can someone help explain why does this happen? Thank you!

math – Need help for beginners in Java

Hi there i am new in java,
I am trying to get result of this.
public class Main {

public static void main(String() args) {
    int a=9+3;
    int b=a-2;
    int  c=b*4;
    int d=c/2;
    int e=++d;
    int  f=--e;
  int g=e%3;
    System.out.println("a:"+a+" "+"b:"+b+ " "+"c:"+c+" "+"d:"+d+" "+"e:"+e +"f:"+f+" "+"g:"+g);
}

}
it gets this answer:a:12 b:10 c:40 d:21 e:20f:20 g:2
why am i getting this result??d must be 20 and e must be 21
if i change d and e into this

public static void main(String() args) {
    int a=9+3;
    int b=a-2;
    int  c=b*4;
    int d=c/2;
    int e=d++;
    int  f=e--;
  int g=e%3;
    System.out.println("a:"+a+" "+"b:"+b+ " "+"c:"+c+" "+"d:"+d+" "+"e:"+e+""+"f:"+f+" "+"g:"+g);

}

i get result of a:12 b:10 c:40 d:21 e:19f:20 g:1
I know it is very simple and basic but i cant figure why?Please someone help me.

contest math – Number of times creepers will meet while climbing a cylindrical pillar.

Two creepers, one Virginia and the other Wisteria, are both climbing
up and round a cylindrical tree trunk. Virginia twists clockwise and
Wisteria anticlockwise, both start at the same point on the ground.
Before they reach the first branch of the tree the Virginia had made
exactly $4$ complete twists and the Wisteria exactly $7$ twists. Not
counting the bottom and the top, how many times do they cross?

How can we solve this? Please help !!!
Not able to think of a way.