Htydjtk

As the title says it is a compete the sequence.

My thoughts:

From all the circle ones that aren't a circle, you can make a circle by rotating the pieces. From all the triangle ones that aren't a triangle, you can make a triangle by moving one line. But I can't figure out a rule for the square-ish things. (Of course the rules I came up with for the circle and triangle might be wrong.)

I'll go with:

Why?

There's a triangle, a circle and a 'U' shape. They each appear both 'normal', once with both halves mirrored along a vertical axis, and once with the left side intact and the right rotated 180 degrees.

Based on what's there already:

the three states for triangle and circle, and both the normal and mirrored state of the 'U' shape

what we need is:

left side of the U intact, right side rotated 180 degrees.

I think it is the,

Third one in the first row

There is a circle, a mirrored half of a triangle, and an upside down T in each each row


The first row is correct


The second row, you cut it vertically and switch the sides


The third row, you cut it down the middle vertically and flip the right side over the x axis and the left side over the y axis


The reason it isn't a circle, triangle, and U is because of the second row. There is no way to move the triangle and U to get the circle while preserving their shape, therefore, they need to move the same way the circle will which gives you the shapes in the first row. the rows do not have the same moves to get to the end result although they do build on each other in number of moves. The first row has 0 moves, the second has 1, and the third has 2.

It is

the third one in the first row.

Let's look at the triangles:

Row 2, Column 2: First picture: the intact triangle

Row 3, Column 2: Second picture: right half of the triangle has been rotated horizontally and vertically

Row 1, Column 3: Third picture: other half of the triangle has been rotated horizontally and vertically, afterwards that whole picture is again rotated horizontally

And now for the circles

Row 1, Column 2: First picture: the intact circle

Row 3, Column 1: Second picture: half of the circle has been rotated horizontally and vertically

Row 2, Column 1: See: half of the circle has been rotated horizontally and vertically, and then again rotated horizontally

Aaaand finally the .. squarish things?

Row 2, Column 3: intact U

Row 1, Column 1: again, rotating the right half vertically and horizontacally

That is the one in the new Row 1, Column 3

Row 1, Column 1: final picture

You can also see a pattern in the rows and columns:

Triangles

Rows: 2, 3, 1

Columns: 2, 2, 3

Circles

Rows: 1, 3, 2

Columns: 2, 1, 1

Squares

Rows: 2, 1, 3

Columns: 3, 1, 3

So all in all it's this:

Rows are: 1,2,3 - 1,2,3 - 1,2,3

Columns are: 1,1,2 - 2,2,3 - 3,3,1

Cheers.

1.3

Divide image in half, flip half; and reconstruct the whole image.