$4$ bugs are placed on $4$ square vertices ,

Where the bug number $i$ is placed on vertix number $i.$

If the day is $\left\{sunday,wednesday,friday\right\}$ , the bugs will go cloclwise such that the bug number $1$ will go one step , the bug number $2$ will go two steps , the bug number $3$ will go four steps , the bug $4$ will not move.

If the day is $\left\{monday,tuesday,saturday\right\}$ , the bugs will go counterclockwise such that the bug number $1$ will go four steps , the bug number $2$ will go three steps , the bug number $3$ will go five steps , the bug $4$ will not move

If the day is $\left\{thursday\right\}$ , the bugs $1,4$ will not move , the bugs $2,3$ will go $2$ steps clockwise .

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Today is sunday , and the bugs didn't start moving yet
**

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step is the length of one side of the square
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In which day of the week "at the end of the day" will the four bugs be on the same vertix for the first time ?

$tuesday$
This will not happen
$sunday$
$friday$

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Sorry , my english is not perfect ,

The difference between the bugs $2,3$ is odd at the start , every day , the difference between these two bugs will be changed by an even number , so , they will not be on the same vertix in any day , which means , that the four bugs will not be on the same vertix at the end of any day 😀