# Progressive matrix: 3x3 grids with yellow, red, or blue cells

This is the final question(No 30) from an IQ test https://docs.google.com/forms/d/e/1FAIpQLSfSn2jji4_n8ef-A3uhwhBrzuAViybyAgQj1Umaf1csP7KJfA/viewform

Personally I think it is A. The last pic should have only 3 yellow squares, 1 blue and 1 red. And if we see the columns, the blue becomes yellow on the right below square on the same position and if we see rows the blue becomes red in the right next square in the same position.

First thing to notice:

The first row are column headers, the first column are row headers.
The remaining squares are constructed from these headers.

From there I see two patterns:

The yellow cells are the XOR of the row header and the column header. Possibly covered by a red or blue cell.

Where there is a blue cell in a square, there is a red cell in the next square on the right or below.

From these you can conclude:

The red cell placement only leaves A as a possible answer. That option is also compatible with the rule for the yellow cells.

There might be an additional rule telling where the blue cells are. I haven't found it.

Update: I got it wrong! Here is the correct answer:

The yellow cells are the XOR of the row and column headers. That is still OK.

The red cell covers the first or next white square after the position in the previous square.

The blue cell covers the first or next yellow square after the position in the previous square.

So the correct answer is E.

• I find it really unsatisfying that the red/blue squares follow a rule that treats the table as a list. Each entry in the table is therefore not defined only by its headers, but also by the "previous" entry in the table. Bah humbug! Nov 24, 2023 at 14:54
• Agree. And the fact that a solution looks good but ends up being wrong because there is a arguably "more correct" one isn't nice either. Nov 24, 2023 at 15:03