Eli5, How do these work and how could you make stuff like this?

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I saw this:

[https://youtu.be/ikbEBp5BeCM] and several other videos that have a similar style, but exactly is it made. Is every possibility just accounted for, or is there a system, or a trick to it?

In: Mathematics
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The trick is that you are forced onto that square by the moves your allowed to do. No matter what square you start on following the sequence of allowed moves will put you on that last green square.

Just look at what every action does. The first one already forces you to the top left corner, or one of the pink squares of the second column.
The second one brings you to one of the 2 green squares on row 1, column 2, or row 2, column one. The third one moves you to either row 2, column 3, or row 3, column 2. Finally, the fourth move brings you to the losing square.

The basic idea is to give choice, and slowly eliminate that choice. Like, select one of three squares. Then move to right if you can, or to the left if you cannot. Now, you have squeezed original three choices down to two, either middle square or right-most square. Similarly you can slowly just squeeze the choice away until every choice has been forced to the same result.

What I like to do with these is pick two initial choices, and follow both. It’s fun seeing them being brought closer and closer together until at some point, both choices end on the same place, and the magician reveals their prediction.