eli5 Why do plastic products sometimes have a clock sort of thing on them

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The title. Also why does some cardboard packaging sometimes just have random colors in one small area

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Both of those are for quality control checks.
The clock tells you when the plastic thing was made. So if the plastic part factory starts discovering a lot of “bad” parts they can hopefully use that information to track down the cause.
The “random” colors are to check for problems with printing. They’re usually setup to let the printer check that the darkness of each color is correct, and to check that the different printing steps all align with each other correctly.

Most plastic parts are molded. So there is two or more mold halves that gets filled with liquid plastic which then harden. These molds last a long time and is very expensive to make. But that means that if you want any kind of variable text on the plastic then it would be too expensive making a new mold every time you change the text. There fore they have inserts which are put into the molds and can be easily replaced. But even these are quite expensive and will last a long time. So to save on inserts they have the same insert but allow it to rotate to point to different numbers. It is often a manufacturing date or a batch number but can be anything. It helps them keep track of the different parts down the line and might help them identify which parts are affected by a quality issue. Say they notice that some plastic parts break under testing and they suspect the plastic mix was bad, they can then compare these number on the parts that broke.

The random patterns of colors on printed material is there to easily notice if the ink have run out or if there is any issues with one of the colors. It might be hard to detect any printing errors in an image, especially if they are doing lots of random prints one after the other. But by printing the same color markers on everything they can quickly see if it was printed right. If these color patterns are printed as it should they assume the rest of the print is also good.

Quality control.

The clock on moulded parts is used to indicate when a part was produced, or what production run.
This can be used in various ways – for example a builders hard hat is only guaranteed as effective for a certain length of time, so the mark is used to indicate the manufacture date so you know when it should be removed from circulation.
In other cases it can be used to pinpoint a particular mould or production run if problems are discovered and so on…

The coloured blocks on printed media (cardboard boxes, newspapers, etc) is a test for the inks used in the printing – if you see the full set of colours (cyan, magenta, yellow plus blacks) and they all look correct then your print run is correctly calibrated, if there is a problem with any of them then there is an issue that needs corrected.