# Mensa sample IQ test questions - 3x3 grids with shapes, 4x4 grids with colored cells  I found these questions in a sample IQ test for Mensa. Any ideas?

Source: Mensa Denmark IQ test

For 37, the answer is:

H

The reason is:

Define a priority system where if there's multiple colors in a cell, the one with the highest priority is shown. If there's a tie in the priority, it alternates which one is shown on top. There are a few separate patterns here. The gray cells gradually fill the entire screen diagonally and has the highest priority (i.e. will cover any color below it). Across the 9 grids, the red cell is at the x-th position of the grid, where x is defined as follows:

 1 2 3
6 5 4
7 8 9
There are 2 blue cells starting at the first and third position (in the first 4x4 grid the first blue cell is covered by the red) and moves forward 1 cell per grid. These 2 blue cells are to be treated separately, let's name them B1 and B2. For the priority of red, B1, and B2, they have the same priority, with red always being the first one to be shown. (Grid 1- Red > B1. Grid 3- B1 > Red. Grid 4- Red > B2. Grid 8- Red > B1. Hence for grid 9- B1 > Red) In grid 9, the blue cells will be at position 9 and 11. Since it's B1's turn to be on top, the answer is H.

Edit: The answer for 39 is:

F

The reason behind that is:

Within the same row, the left 2 columns shifts right by 1 column, and undergoes the substitution Triangle -> Square, Square -> Circle, Circle -> Triangle. The right column becomes the left column and does the same substitution, however, it is rotated down by one. i.e.

 1    3
2 -> 1
3    2
Across different rows, (e.g. 3->4, 6->7) the pattern simply rotates clockwise.
Hence, the final answer is F.

• Thanks for answering, but I don't really get your explanation on the red cell's movement. Also do you suggest that the priority with which red and blue cells appear is changing every time? Aug 18, 2018 at 13:03
• The red cell occupies the 1st, 2nd, 3rd, 6th, 5th, 4th, 7th, 8th, 9th cell respectively for each of the grids. The priority between the red cell and the first blue cell changes every time. (It overlaps the first blue cell 4 times, in the 1st, 3rd, 8th, and 9th grid) This is calculated separately from the interaction between the red cell and the second blue cell as they only overlap in grid 4. Aug 18, 2018 at 13:09
• @giannispapav Follow the trail of numbers that red follows in the matrix mentioned in the answer and you will notice the pattern Aug 18, 2018 at 13:58

I believe there is a less complicated explanation for #37:

The red and blue squares move one step to the right for each image. From the last column they move to the first column of the next row. They are hidden by the gray squares, and when hidden they change color (red/blue). The correct answer is F.

puzzle 39

The correct answer is F

Explanation: Looking at a row each tile is shifted once to the right and turned in a pattern like this: (squares becomes circles) (circles becomes triangles) (triangles becomes squares). The last column of a picture when its shifted towards the right: it shifts one downwards before appearing on the left side of the new picture.

For puzzle number 37, I believe it's

The number of grey cells stars with zero and increases by one each time. Answer H has 8 grey cells.

• All answers have 8 grey cells. What makes H the right answer? Aug 18, 2018 at 16:16
• There is already an accepted answer that proposes H for puzzle #37. Before answering, take a look at other answers. Aug 18, 2018 at 20:42
• @xhienne I'd like to see other answers if there are any. But this one is not accurate enough. Aug 19, 2018 at 14:18
• @giannispapav Exactly. Same answers with an alternate reasoning are welcome here. But this answer provides no reasoning at all, which boils down to repeating what the accepted answer already stated. Aug 19, 2018 at 15:44