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Virtually all puzzles in The Witness have some sort of underlying logic. However at the start of the game there is a cylinder pillar puzzle that has no identifiable logic or solution, just two rows of upward pointing triangles from top to bottom.

All game walkthrough solutions indicate that multiple turns are needed to solve it, but there is no symbolic marking on the pillar show these turns.

Some puzzles use environmental references nearby, but there are no identifiable nearby objects that help to solve the column.

What am I overlooking?

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    I am not sure which one you mean. I can think of several puzzles in "The Witness" which could be described as "Pillar Puzzle", but none that are directly at the start of the game. Perhaps you can take a screenshot?
    – Philipp
    Commented Jun 12, 2023 at 8:05
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    By the way, a recurring game design motive in the game is to occasionally confront the player with puzzles that are still far too complex for them to solve, but then later become easy when the player learned more about that kind of puzzle in a different area of the game. The player is expected to pass on such puzzles for now and return later when they learned the mechanics.
    – Philipp
    Commented Jun 12, 2023 at 8:08

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A pillar in the Entry Area adorned with triangle symbols (see the screenshot below) is actually a puzzle that activates another larger puzzle on the ground nearby. Solving both counts towards the main puzzle count.

enter image description here

As you will learn, in order to complete triangle puzzles:

the cell containing the triangle must be surrounded with a number of lines equal to the number of triangles within the cell.

And as far as I know there is no dedicated tutorial area for triangle puzzles.

If needed, here is a complete walkthrough.

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Strike "virtually" - ALL puzzles in The Witness have some sort of underlying logic, that's the whole point of it, and the major aspect of why the game is absolutely ingenious. There is no luck factor (with one single exception), only learning and understanding.

Even the

time challenge in the hidden area

at the end REQUIRES you to actually have understood all puzzle rules, you cannot solve/cheat through it with a walkthrough (you can only get two or three slightly helping hints from those), you HAVE to be able to actually master each puzzle type. That's ingenious (and most likely quite annoying for many players ^^ ).

Now, to answer your question: there IS a tutorial in the game for the triangles. Only it's not situated at a particular place. You need to actively explore the island, as the hints are scattered all over the island on "random", seemingly useless single panels just lying on the floor, sometimes halfway hidden. But they do teach you all you need to know about how the triangles work.

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