# Mensa question 29: 1-3 black or white boxes on either side of a vertical line

Anyone happen to know how this works? We can't decide whether to go top down or left to right.

• Where is this mensa test? Apr 17 '20 at 12:03
• This puzzle might be harder for people reading from right to left...that would mean different operations in the right-to-left direction than in the top-to-bottom direction. Apr 18 '20 at 8:19

C

because

Treating squares to the left of the line as negative and squares to the right as positive, and counting black and white squares separately, the number of squares in the right column is the sum of the squares in the cells left of it, and the number of squares in the bottom row is the sum of the squares in the cells above it.

• Sweet that's what we figured as well. Thanks! edit It does appear to work the same way left -> right as well, I believe Apr 16 '20 at 21:56
• Yeah, the point of "We can't decide whether to go top down or left to right" is that you don't need to decide because a correct solution works both ways. Apr 17 '20 at 17:43
• You can also view the figures as representation of "fraction". "Black" and "white" squares are coprime numbers, when on one side of the bar they're part of the product. Third(right) column is the result (reduced) of multiplication of "fractions" from the first two columns. And third(bottom) row is the result(reduced) or multiplication of "fractions" from first two rows. Just remember how to multiply and reduce fractions and that would be easy to solve. Apr 17 '20 at 18:27

If we treat each bar divised group as a number, with left side as positive and right side as negative value, then:
First cell "plus" second cell equals third cell -> black squares on left are added while two white squares on left and right nullify each other.
This is also true for first row "plus" second row equals third row.
The last cell is thus
Horizontally: 1B 1W | 0 "plus" 0 | 3W = 1B | 2W
Black white "plus" negative three white. Black remains, one white gets nullified, two whites remaining on right side, giving "Black | 2 white"
Vertically: 2B | 0 "plus" 0 | 1B 2W = 1B | 2W which is the same as horizontally.
Caveat: In all but one cell the Black square is always on top of white ones. Yet the middle cell has Black square underneath white. It could mean the order is also important here, but then I have no theory how it would work.

Answer C - 1B | 2W, but unsure.