# Continue the Pattern

Another one of my puzzles to promote our school's webpage that has no answer yet after a week:

Not very solid logic but I would say:

My explanation below:

First and last column seem to be opposite sides of the dice and no other sides have the exactly same orientation (the 2's and the 3's are turned 90 degrees). So pretty much builds the pattern between 1st and 3rd column and use the 2nd one to not match the orientation of any single die.

• I think you are essentially correct in your deduction, although OP probably was thinking about rolling the same, slightly non-standard dice on each row. – Bass Jul 20 '18 at 9:18

I would say that the correct answer is

C

Explanation :

The set seems to be a collection of all the different patterns you can get on the faces of a 6-face dice, allowing center rotations.
Thus, you can have only one representation of 1, 4 and 5 as they remain identical when you rotate them, but 2 versions of 2, 3 and 6.
The one that is missing from the set is therefore C

• Hello, that is pretty much my answer though I saw another pattern that reaffirms it – Ontamu Jul 20 '18 at 9:34
• Well, I only read the beginning of your answer (the part where you mention opposing sides) before posting my answer, so I didn't noticed they were similar (though " no other sides have the exactly same orientation" misled me because for me, every side has 4 orientation, which may share the same pattern, thus, it did not struck me of any similarity) – L.D. Jul 20 '18 at 10:20

It is

The following explanation reveals why some faces of each die are rotated... it took me a while to come up with a plausible answer, so thanks OP for the puzzle. It was great! :D



## Explanation:

We will look at the faces below,

and compare it with a net of a single die; i.e.,

Look at the rows of the faces. The first row is

In the net...

...when drawing a line from the $4$ Face to the $2$ Face in the net, you want to then draw a symmetrical line from the last met Face (i.e. the $2$ Face). This will mean you have to draw a line from the $2$ Face to the $3$ Face, thus making the $3$ Face come last in the row.

Let's rotate the net $90^\circ$ clockwise ($90$ degrees to the right):

And look at the second row in the given faces.

In the net,

...when drawing a line from the $2$ Face to the $6$ Face in the net, you want to then draw a symmetrical line from the last met Face (i.e. the $6$ face). This will mean you have to draw a line from the $6$ Face to the $5$ Face, thus making the $5$ Face come last in the row.

Now we rotate the net once more, $90^\circ$ clockwise:

And look at the third row in the given faces.

Oh no!

There are only two faces in that row. So what is the last one?

Well,

Using the same rules, we look at the net...

...when drawing a line from the $1$ Face to the $3$ Face in the net, you want to then draw a symmetrical line from the last met Face (i.e. the $3$ face). This will mean you have to draw a line from the $3$ Face to the $6$ Face.

This means,

The $6$ face finishes off the incomplete row. But it is rotated because we rotated the net!

Therefore,

The answer is $C$.

...either $B$ or $E$



## Original Thought:

Convert the numbers of dots on each die to, well, numbers.

$$\begin{matrix}\boxed4 & \boxed2 & \boxed3 \\ \boxed2 & \boxed6 & \boxed5 \\ \boxed1 & \boxed3 & \boxed? \\ \end{matrix}$$

Now we carry out the following calculations:

\begin{align}4\times (2+1)\tag{for the leftmost column}&= 12 \\ 2\times (6+3)&=18\tag{for the middle column}\end{align} so we have the pattern $12, 18, 24$ such that $3\times (5\,+\,?)=24$ (for the rightmost column).

That leaves the answer to be,

\begin{align}?&= (24\div 3)-5 \\ &= 8 - 5 \\ &= 3.\end{align}

So now we know,

The answer is either $B$ or $E$, because they each have three dots.

• (+1) Wow! How long did you spend on typing this? – TheSimpliFire Jul 21 '18 at 10:00
• @TheSimpliFire hahah, I don't know — but it was long. I am convinced this answer is correct... well, I am hoping ;) – Mr Pie Jul 21 '18 at 12:03

E

Explanation:

Add the values of the first row: $4+2+3=9$ is odd.

Add the values of the second row: $2+6+5=13$ is odd.

This means that the total of the third row must also be odd, which eliminates A, C, D and F.

For the first column, every single one has dots on the top-right and bottom-left, except for the bottom square.

For the second column, every single one has dots on the top-left and bottom-right, except for the bottom square.

For the third column, the top two squares have dots on the top-left and bottom-right, so the bottom square must not have these properties. Hence B is eliminated.

• I didn't know you could write <!>. I thought you could only write <sub></sub> and some other block-quote command I don't remember :) – Mr Pie Jul 20 '18 at 9:06
• @user477343 I'm the total opposite. I don't know anything about blockquotes ;) – TheSimpliFire Jul 20 '18 at 9:06
• @user477343 Just realised that SE changed the colour of the comment upvoting button and the editing sign... – TheSimpliFire Jul 20 '18 at 9:08
• I think the upvoting button for comments is blue, now. The normal upvoting system (for questions and answers) use to be red, I think, once upon a time :) – Mr Pie Jul 20 '18 at 9:08
• I have not looked at the other answer, but I am gonna have a go at this problem. With number problems like these, there seem to always be more than one solution :D – Mr Pie Jul 20 '18 at 9:10

F

Explanation:

If you take a regular 6-faces dice and you begin with the first face of each row and you follow the path created by the second face from that row, you'll get the the third face:
For example, the first row creates this pattern: 4 -> 2 -> 3 -> 5 -> 4 -> ...
To explain it more, make 4 face up. Now rotate the dice to make 2 face up. Perform the exact same rotation again, and now 3 is facing up. Et voilà!
Same works for the second row. And for the third row, that yields a standing 6, i.e. F.

If you don't have a real dice, try to wrap your head arround this image.

• This answer looks pretty good as well, though my answer is similar to yours. $(+1)$ – Mr Pie Jul 21 '18 at 9:01