# Identify the next symbol in the pattern

## Which symbol should replace the question mark in the above pattern?

To clarify a few things:

• You can solve this puzzle with a printed version of it; that is to say, there's no steganography or other means of encryption involved here.
• The square layout of the tiles is irrelevant. They go in a specific order, and this puzzle could just as well be solved with the tiles laid out in a straight line.
• There is no 'misleading' information in the puzzle. Every single piece of the puzzle is relevant to its solution.
• The pattern will be obvious once you discover it. If at any point it feels like a stretch, or you seem uncertain about anything, you're on the wrong track.

Hint 1:

Try not to get too caught up on the word pattern. Looking for patterns in the colors will most likely not get you to the right answer.

Hint 2:

1 2 3
4 5 6
7 8 9

Hint 3:

This puzzle would work in black and white - the colors simply add a nuance.

• I feel like the answer should be B, but I can't justify it. – Joe Z. Jun 16 '15 at 3:10
• The square layout of the tiles is irrelevant. They go in a specific order... Then I think you should clarify the order. Should we read these tiles by rows or by columns? The answer given by Player One assumes reading by columns (where 1 yellow + 3 purples was 2nd tile), but my natural tendency was to read by rows (where 2 blue + 2 orange was the 2nd tile). – splungebob Jun 17 '15 at 19:39

The dots are a binary representation of the digits in the golden ratio (1.61803398), with each primary color representing a 1, and secondary colors are a 0.

So,

0001 0110 0001 1000 0000 0011 0011 1000, and the only block that could be 1000 is B, Yellow Purple Purple Purple.

Edit: looks like I was beaten.

Second edit:

the primary/secondary color pairs are also opposites on the color wheel. Starting with '1', the colors cycle through red yellow blue as the digit's primary color for the binary encoding

• You added a bit of explanation about the colors. I'll +1 your answer, but I'll accept the first answer than can explain exactly how the colors were chosen to represent their specific numbers! – Bailey M Jun 24 '15 at 19:40
• @baileym added another note about the colors – dfperry Jun 24 '15 at 19:42
• @baileym also, you said the puzzle would work without color, so wanting specific color pairs for each digit is kinda off, don't you think? – dfperry Jun 24 '15 at 19:46
• What I meant was that the base idea of the puzzle didn't involve the colors. The colors are a secondary part of the puzzle, which do have a reason to their rhyme as well. – Bailey M Jun 24 '15 at 19:52
• starting with '1', the colors cycle through red yellow blue as the digit's primary color for the binary encoding – dfperry Jun 25 '15 at 12:37

An attempt of an answer is B because

Splitting the pattern into 9 "fields", each field consists of two "complimentary" colours. Red/Green Blue/Orange Purple/Yellow. Each of the fields is either a duplicate or the colour-inverse of another, with the central all-green tile being an exceptional piece. (As there are an odd number of tiles, one has to be a "stand-alone" item. Central and of one colour only seems to be an appropriate choice.) This leaves the tile which looks like the "B" tile to require a double or an inverse, and tile B is the only one fulfilling this requirement.

A simpler way of seeing it:

All tiles on the left need a duplicate on the right. The central column is symmetric and otherwise just a distraction.

• While this is certainly valid reasoning, it is not the explanation I'm looking for. Each tile is meaningful to the final solution. :) – Bailey M Jun 16 '15 at 16:03
• I was afraid it would be so. Not seeing it (yet) though. – BmyGuest Jun 16 '15 at 19:37

It can only B

the decimal digits of the golden ratio, expressed in binary

• That's more like it. :) Can you explain the color scheme? – Bailey M Jun 24 '15 at 19:30
• If you're treating zero as the last digit (for toots and giggles maybe), then I would guess two and five should be yellow/purple while four and seven should be red/green. – Jared Jun 25 '15 at 10:32

Well their is so much data that can prove it, that will take at least one hour to enumerate all of them, so I will just write the most obvious one:

You need to calculate the number of identical colors from the start of each symbol until they change.here the pattern: 3|1|3...1|4|2...2|1|4 (each row must be equal to 7)

"The square layout of the tiles is irrelevant."

So now, the answer is B:

You need to calculate the number of colors switching in each tiles, the pattern is: 1/2/1/1/0/1/1/2/1

First, we need to now what we have here: 6 different colors, 8(+1) tiles, 4 colored circle in each tiles, Only one colored circle can link another one, only one tiles is fully filled with only one color, colors have their own pattern (green + red, orange + blue, yellow + purple), only the (orange + blue) pattern are equal (2 of each of them in their tiles). Now, we can start conceptualizing the pattern by asking some question: does those colored circle linked each others mean we need to read them like this (bottom-left > top-left > top-right > bottom-right) ? If yes, does we can say they are like rainbow ? If yes, RED=1,ORANGE=2,YELLOW=3,GREEN=4,BLUE=5,PURPLE=6 ? If yes, does that mean that each color pattern is equally distanced by 3 (Green = 4 / Red = 1, Orange = 2 / Blue = 5, Yellow = 3 / Purple = 6)? If yes, that mean 3 must be our delimiter for calculating our pattern ? If yes, can we say that we need to read 3 tiles by 3 tiles ? If yes, we can easily see that each of those 3 row of tiles are hugely different in term of colors and number of same colors, right ? If yes, does we will need to read by a logical order following the "arc / rainbow line" ? If yes, that will mean that the type of colors, the color at the start/end and the order of them in the tile is Irrelevant ? If yes, this will indicate that only the colors switching is relevant ? If yes, how can we calculate it ? Maybe, by giving to each tile a point for every color switched, in example: (green,green,green,red = 1) / (orange,blue,blue,orange = 2) / etc.... By this theory, only one symbol can be our next symbol in the pattern: B --Since B is the only tiles with 1pts color switching in those suggested symbol.

• Welcome to Puzzling zaykho. This is a good start to a solution, however I suggest that you add more explanation behind how your answer works and how others can use your answer. – Mark N Jun 17 '15 at 18:24
• I do understand your solution (and like the idea.) If English is hard, you may also try a visual solution. Draw (or copy & modify) the image and add the numbers... – BmyGuest Jun 18 '15 at 6:39
• Added a new answer after reading this : The square layout of the tiles is irrelevant. Also, I have detailed to the maximum (took 20 minutes to post lol)! – zaykho Jun 18 '15 at 12:56
• Also, with this theory, whatever how we read it (by column or row) the final pattern is always good ! – zaykho Jun 18 '15 at 13:04

If we read the squares in order as

147
258
369


Then the patterns go (with bold as the start of a repitition and italic as the inferred next in series)

Green/Red:

green+red, skip 3, all green, skip 1, green + red, skip 3, all green, ...

Purple/Yellow:

Not really much information on this one, but skip at least 6

Orange/Blue:

Orange left + blue right, orange bottom + blue top, skip 1, orange top + blue bottom, skip 1, orange left + blue right, orange bottom + blue top, skip 1, ...

Therefore I think the answer is

D

• I added a clarification on the puzzle itself, but to make sure you see it: "The pattern will be obvious once you discover it. If at any point it feels like a stretch, or you seem uncertain about anything, you're on the wrong track." :) – Bailey M Jun 17 '15 at 15:31

Reading each unit as a series of four colored nodes, the number of color changes in each unit is represented below in square form:

121
101
12?


As zaykho points out, there is clear symmetry here no matter whether you read the units left-to-right, up-to-down, or as a square. Only one of the options fits this symmetry:

Answer B, which has 1 color change.