# Find the missing item in this grid

Here is a 4x4 grid whose items follow a certain pattern:

Can you find the symbol and color of the missing square?

Edit: All items in the square follow the pattern. There are no useless squares and changing any square would make the puzzle not work.

Hint 1:

The pattern you're looking for should allow you to generate the whole grid using only the first symbol.

• The green areas look like a moose. Just sayin – Avigrail Aug 2 '16 at 10:27
• About dashes, does it matter if they are em dash, en dash or hypen? Or is it something we should find out? Of course if this is too much to ask, you can just say, no comment. – Lafexlos Aug 2 '16 at 10:54
• @Lafexlos: They are just lines in different orientations. The possible answers for the last cell would be "-", "|", "\", "/", in either green or red. – Runemoro Aug 2 '16 at 12:14
• @runemoro .... "/" is a valid line??? you didnt say so. as its missing, is as logic as "%" – lois6b Aug 2 '16 at 12:35
• @lois6b: All I'm saying is that you need to think of the symbols as lines rotated in different ways, not as "-", "|" or "\" characters. – Runemoro Aug 2 '16 at 18:18

A green "--". Going from Ryan's comment that this looks like a rotation puzzle and from the hint that the whole puzzle can be generated from only the first symbol, the rotations for going from one cell to the next (horizontally) are, in 45 degree steps, "2, 3, 1, 3, 3, 1, 1, 3, 3, 1, 3, 1, 1, 3".

Since the lines don't have an arrowhead, that sequence is the modulo 4 of the sequence we're looking for. Looking it up in OEIS gives us "a(n) = n-th prime modulo 4". That means that to go from each cell to the next, we have to rotate it by nth-prime * 45 degrees.

• You got it! Great job! – Runemoro Aug 9 '16 at 16:22
• So, there would have been $/$ symbols if the grid had just been continued two more rows. – Peregrine Rook Aug 9 '16 at 18:46
• How is the color decided? – Ryan Aug 10 '16 at 19:03
• Where do the numbers 2, 3, 1, 3, 3, 1, 1, 3, 3, 1, 3, 1, 1, 3; came from? – Rahul Bali Aug 27 '16 at 14:12

I don't have an answer yet, but the color of the squares just show if the symbol is the same as the symbol in the square above it (green = same symbol, red = different symbol).

That tells us that the missing square is not a "|". The choices left would be a green "-" or a red "\".

• as my answer was "green -" and was incorrect... " red \ " is the one? – lois6b Aug 2 '16 at 12:31
• Good job, PuzzleAnswerer, that's a good start! lois6b, not necessarily, your answer was incorrect because of the explication. The answer may or may not be "--". – Runemoro Aug 2 '16 at 16:26
• reminds me of a Rotation pattern. as if it is rotating somehow – Ryan Aug 2 '16 at 18:16
• If it was incorrect because explanation, can you read my two new ideas? – lois6b Aug 2 '16 at 18:23
• That rotation seems especially prevalent from top to bottom, left to right. Matching the Greens below reds are always the same, but reds are always different. – Ryan Aug 2 '16 at 22:05

because: (WRONG)

the second column is moved one down

Update: (wrong)

Green - If you devide the Square into 4 parts with each having 4 cells then in each square you will find three same color and one different.(answer by Ali786)

Horizontal line. Because horizontally, there are no two repeated cells together, always different. And vertically if you group 3 cells, there are never 3 different cells, always 2 the same (side by side) and other (could be the same too)

Update 2 :

Green - the color of the squares just show if the symbol is the same as the symbol in the square above it (green = same symbol, red = different symbol). (answer by PuzzleAnswerer)

Horizontal line. Because horizontally, there are no two repeated cells together, always different. As the color of the top right corner is red, it means the line is not "|" . So the unique element posible is "-" as to it's left has "\"

• In that case how do you explain the relation of the first and third columns? – The Dark Truth Aug 2 '16 at 8:01
• It works, but that's not the answer I had planned. The pattern I'm talking about should be able to explain why all the squares are the way they are. Your answer also doesn't use the first column... Sorry, but nice try! – Runemoro Aug 2 '16 at 8:02
• ouch, i'll keep trying – lois6b Aug 2 '16 at 8:03
• i updated it. can you check OP? – lois6b Aug 2 '16 at 10:21
• (Spoiler warning: this comment contains part of the answer.) @lois6b: +1, because you were (apparently) the first person to point out part of the pattern: the same line orientation never occurs in two horizontally adjacent cells, even assuming that the rows of the grid are adjacent. For example, you never have two diagonal lines side-by-side. It’s too bad that you didn’t notice that you never have two non-diagonal lines side-by-side except for the first two cells; that would have helped. (I’m not criticizing you; I didn’t see it either. I’m just saying you came close to finding a good clue.) – Peregrine Rook Aug 9 '16 at 18:48

Putting everything together:

'green -'
As mentioned before, a square's color shows if the above symbol is the same (green) or not (red).
+ this also works if we go through columns repeatedly i.e. start again at the top.

Therefore:

'red |'
wouldn't be possible since the first on the top right is also a 'red |' (would have to be green instead).

• I thought of posting the same, but we should not be able to change any single currently given square and still have the puzzle work ("changing any square would make the puzzle not work.") - here we could change the green "|" in the right column to a red "\" and get the same solution. (The question is, does that count as what was intended by the comment?) ...Plus 1 though. – Jonathan Allan Aug 3 '16 at 2:53
• @JonathanAllan I agree. I'm still working on horizontal stuff ;) – Avigrail Aug 3 '16 at 5:03
• Why couldn't the answer be a red "\"? – Runemoro Aug 3 '16 at 5:04
• Because I'm still missing something it seems. From what I have it could also be red \, yes. You of all people should know :D – Avigrail Aug 3 '16 at 5:06
• @Runemoro anything to do with hands? – Avigrail Aug 3 '16 at 15:02

Going from PuzzleAnswerer's clue, it is probably:

Red \, since this would create an equal number of red/green squares, an equal number of - or | squares, and exactly 8 \ squares, while following the rule.

• This would not make an equal number of red/green squares. There would be 9 green and 7 red. – Keeta Aug 2 '16 at 18:42