# Cannot see the pattern

Some patterns I could not complete in the IQ test from this website. Can someone explain them to me?

Let's order the answers in this way

 A B C
D E F


PATTERN 3 My guess here was C because the left square in each row seems to add to the second one(??) PATTERN 4 Got dizzy looking t this one. PATTERN 5 My (hail mary) guess here was F because in the previous examples the dashed line never moved. • I know it's not a fun way to get the answer, but we've actually had #3 on here before – Lord Farquaad Jul 11 '18 at 12:35
• And there was recently a duplicate of a much older post with #5 – hagfy Jul 11 '18 at 14:01
• Has a correct answer been given? If so, please don't forget to $\color{green}{\checkmark \small\text{Accept}}$ it :) – Rubio Jul 12 '18 at 5:03
• @Rubio Actually all the answers are correct. Which one should I accept? SMR gave 3 answers but turns out that 2 of them were already been answered. Should I accept Anton's answer(s) then? – shamalaia Jul 12 '18 at 7:07
• What answer to accept is entirely at the asker's discretion; usually they pick the "best" answer, using whatever criteria they feel to be best. As I've mentioned previously, some reward the answer that contains the most significant contribution(s), and some choose to reward the answer which is most complete. Ideally, these are the same answer—the person with the greatest contribution also adds the contributions of others, with attribution, to make a single canonical answer. – Rubio Jul 12 '18 at 7:36

## 3 Answers

The answers are

D, D, E, F and F

Patterns 1, 2 and 4: see the answers of @Anton and @Hans

Pattern 3:

E if we understand the row operation being a truncated sum with values 0 if nothing, 1 if intermediate and 2 if high. A column interpretation would yield the same result but with a flipping operation on the second row

Pattern 5:

F because it is flipping top row then xoring with second row

Note that:

this made me realize that if you have c = a xor b then a = b xor c and b = a xor c so you can write the xoring rule in which order you want; for instance Pattern 4 is easier if you look as row 1 = row 2 xor row 3 because in column 2 and 3 this would be a simple addition

• Your "Note" can be seen easily with simple arithmetic. $a=b+c\ (\text{mod } 2) \implies a+c=a-c=b\ (\text{mod } 2)$ as $b=-b\,(\text{mod } 2)$. – Hans Jul 11 '18 at 17:20

Pattern 1 :

bottom left

Start with the black square's lines, rotate the middle square 45° Counter clockwise and combine the lines with XOR.

Pattern 2 :

bottom left

We always start with a square, the pattern seems to be that we take the middle symbol, rotate it 90° clockwise, and reverse it's operation on the line (curve IN <-> curve OUT)

Pattern 4:

F
Let the black square be $1$ and the white square be $0$. The right most matrix is the square-wise modulo sum of the two left ones modulo $2$.

• I.e. the patterns are XOR-ed. In every row, for each little square location, there are zero or two black squares. The same is true for the columns too. – Jaap Scherphuis Jul 11 '18 at 8:00