# Mensa Norway 2019 questions 8, 12, 17, 18, 31

I'd like to verify my solutions for Q8, 12, 17, 18 and 31. In particular, I haven't utilised all the information in each of these puzzles below and want a better explanation for these.

My pick:

C, Seems like column 2 and 3 are just plain reflection in the x-axis, but then the information in column 1 doesn't mean anything? What does it do?

My pick:

(Approach 1) A, See each row, clockwise rotation, 2 black 1 grey. (Approach 2) D, See SW diagonal line. 2 identical shapes, 1 rotated shape. Grey rotates clockwise, black anti-clockwise.

My pick:

F, tangent to the line in column 1 is the acute reflection Axis for col 2 and 3.

My pick:

C, col-wise + symbol represents 90 deg rotation. Row-wise col 1 and 2 is addition operation. Unsure how the shapes are arranged in col 3. But since row 3 is 90 deg rotation to row 1, I guessed C.

I have seen this question discussed in more detail here: Duplication Question But

I'd be happy with D If it wasn't Black + Black = White or Stripe (So, not a function) Since then you can just argue the same for other colours. i.e. W + S = B or W or S. There is insufficient information in this problem, I think A is also a possibility.. At least 3 whites and 3 Stripes are there too and 3 blacks would still make a pattern.

Many thanks in advance.

• Exercise 17 is definitely D, so the rotation moving from column to column or row to row is always the same. – Magma Nov 25 '19 at 20:31
• @Magma, as in (1,y) is (2,y) 30 degs rotation but (2,y) to (3,y) is 90 degs? (and 30 degs for row 2 to row 3). I wasn't sure because of this inconsistent sudden angle changes. – zcahfg2 Nov 26 '19 at 4:59
• 45 degrees, not 30, but otherwise yes. – Magma Nov 26 '19 at 21:46

Here is the best I can do for all questions. They might duplicate, sometime improve other people's answer.

Exercise 8:

C. The top row of dots is copied down and left. The bottom row of dots is copied down an right.
Or: From left to right, the top row of dots follows the pattern 3-2-1-3-2-1, while the bottom row of dots follows 1-2-3-1-2-3.
Or: From top to bottom, the top and bottom rows of dots follow pattern 3-2-1-3-2-1.
Or: Mirror the 2nd column.

Exercise 12

A. The triangle rotates counterclockwise from right to left or from top to bottom,
and There is one gray in each row and each column.
Or simpler: A cell is always identical to the cell up and left.

Exercise 17

D. From left to right rotate 45˚ then 90˚.
Or: From top to bottom rotate 90˚ then 45˚.

Exercise 18

C. From top to bottom: remove a horizontal and add a vertical line.
Or: From left to right add 0 vertical and horizontal line, then add 1 vertical an horizontal lines.

Exercise 31

D. As per the other duplicate question, assuming the bottom squares are a function of the corresponding squares in the rows above, then the middle square must be white and the left and right squares must be identical. It leaves only D.

On question 8 it is c because the pattern goes for for each row 1,2,3 dots on top of the middle row of dots and 1,2,3 dots on the bottom.
Question 18 is saying that if there are more than 3 of the same lines on one row then you rotate one of the lines 90degrees on the last tile of the row.
Excercise 31 Sure the vector explaination works but it could be A because then the sum of the white squares per column goes down one from left to right. The rest of your answers are solid.
Edit: question 17 the answer is d because in the row it rotates 45deg clockwise and then 90deg. Sorry I just glossed over your answer on this one because I thought you got it right since it is so obvious.

• Thanks, I have two potential solutions for q12, which one do you think is correct? – zcahfg2 Nov 26 '19 at 5:07
• A because the shading occupies one corner in a clockwise pattern as you progress through the rows and each row has 2 black and one shade. – Deepthinker101 Nov 26 '19 at 19:24

I think A for 12 simply because if you look at the 5 sets of diagonal lines of symbols starting top left and finishing bottom right. Looks neat and tidy.

Q31 could possibly be A If you consider the colours and line pattern in this order Black.White.Diagonal The total number of Black,White and Diagonal squares corresponds to 8,9,10

B,W,D 8,9,10

18.

Top-left (+) plus centre (=) gives top-right. Top-middle (+) plus bottom-left (||) gives middle-right. So what is left is (||) and (+) for C.