# What is the solution to this square puzzle? Former details linked in question source.

B.

There is actually a combination of relatively easy patterns behind this puzzle. I think the first thing we all should notice is the number of shaded blocks:

The first picture has 1.

The second one has 2.

The third one has 3.

And so on. So that’s the first pattern established.

Next. notice how the are filled. Picture one starts filling from diagonal 1, which is the top-right diagonal.

Picture two, the 2 shaded blocks are on the second diagonal.

Picture three, 3 shaded blocks on third diagonal.

Now picture 4 gets interesting. The pieces start from 4th diagonal since in pattern 3 we have filled up until 3rd diagonal, but only 2 pieces can fit in, and pattern 4 has 4 in total! So another 1 piece moves down to diagonal 5 and the last one restarts at 1st diagonal. In summary:

first 2 pieces — 4th diagonal

next 1 piece — 5th diagonal

Last 1 piece — 1st diagonal.

It’s the same for pattern 5. Starting diagonal of 2 since pattern 4 ended at diagonal 1, and then pieces get carried over to next diagonal after one diagonal is filled up.

So pattern 6 would have a starting diagonal of 4 (pattern 5 filled up to 3) and pieces arrangement as follows:

Fist 2 pieces — diagonal 4

Next 1 piece — diagonal 5

Next 1 piece — diagonal 1 (restart)

Last 2 pieces — diagonal 2

To help you visualise this pattern, you could think of someone painting the blocks diagonally, but in different sets, Pattern 1 represents the first 1 block he paints, then, say, he takes a rest, continues painting where he left off, and this goes on. When he has finished painting one 3×3 block, he moves on to another block.

(Here you see the pattern. The lighter-coloured blocked denote the blocks the painter starts on first.)

I’m going to suggest that the answer is A based on the presumption that the sequence follows the following rules:

• Each grid must have one more purple square than the preceding one in the sequence.
• All squares along each diagonal in the \ direction must be the same color.
• White diagonals below purple diagonals must become purple in the next step, and purple diagonals below white diagonals must become white in the next step.
• Either all the purple diagonals should form a contiguous block or all the white diagonals should form a contiguous block.

If you sit down with a grid and fill in the top right corner, then construct successor squares by satisfying all of these constraints on each step, you will exactly reconstruct the given sequence, with the sixth grid being A as the unique solution. No seventh grid is possible following the rules.

There are 2 other sequences on 3×3 grids following these rules, both starting with a purple square in the bottom left corner. One is otherwise exactly like this one, and the other ends after only a single step. Clearly, these rules are tailored to produce this sequence.

What is the solution to this square puzzle?

We begin by diagonally numbering the cells of a 3×3 grid, from 1 to 9.

Now, the numbers of the purple cells for each element can be given as
$\begin{array}{c||ccccc} 1 & 1\\ 2 & 2 & 3\\ 3 & 4 & 5 & 6\\ 4 & 7 & 8 & 9 & 1\\ 5 & 2 & 3 & 4 & 5 & 6 \end{array}$ .

Following the pattern, the most logical next in sequence appears to be
$\begin{array}{c||cccccc} 6 & 7 & 8 & 9 & 1 & 2 & 3\end{array}$ ,
which is option B.

A
the progression is from upper right to lower left adding a square each time and migrating the rule being turning off the purple squares that were activated the pattern before it, but when we get to 6 activated squares there is no room left to only activate white squares, leaving only A, B or C that follow the progression and have the right number of squares turned purple
I rejected the pattern of squares in each row moving either left or right with the addition of a square after each crossing of the grid, as the bottom row does not follow that pattern, and also rejected movement patterns that show any sort of rotation or pedular movement around any of the vertices or the center of the grid.
reject C because the grid does not follow that the activated squares must try to be switched back off as the pattern progresses (C only activates a 6th square, and the rest do not move
now for the hard part — Why A and not B, if you move the first three purple cubes down they occupy the L shaped corner in both A & B, but if the 2 remaining squares from the previous grid move down also , they would occupy the corners , making the grid a Larger L shape, and the addition of the last purple square would either be in the vacant square at top right, or in the center of the L, — since only one of those patterns is present in the options, it must be correct, which means A is the one that follows the pattern

With my logic, solution is C.

I imagine the purple squares are objects that want to grow and can only move diagonally.

Pictures 1 to 3: first object growing.

Picture 4: the object cannot grow anymore and cannot become smaller BUT still can move down. At the same time the last object reaches the end of the grid, a new object is created. This object follows the same rules.

Picture 5: First object cannot move down, so it goes up. Second object is still growing and moving down.

Picture ‘?’: First object moves up, second object moves down.

It would have two more steps, with a third object coming into play, an it would end there because there is no more room for all objects.

A little illustration of what I mean:

Condition 1: There is increase in number of coloured squares in the sequence.

Condition 2: The progression in colourong is diagonal lines from right hand top corner to left hand bottom corner in a loop.

Only B satisfies both condition.

As we see in the given question, the number of shaded square is increased by one in every next picture, so the answer will have 6 shaded squares. So the option F is rejected.

Now if you see the pattern, you will notice that in every next image the shaded squares move a step forward, so in answer we have to see that it should have 6 shaded small squares and should occupies last second diagonal from the right upper end of the image and all the shaded squares should be in continuation. So the answer is B.

Hope you understand 🙂

In the pattern, blocks adjacent to the blocks filled previously are filled.

2nd box:- 2 are filled adjacent to the one block which was filled in 1st box.

3rd box:- 3 are filled adjacent to the two blocks which were filled in 2nd box.

4th box:- 4 are filled adjacent to the three blocks which were filled in 3rd box.

5th box:- 5 are filled adjacent to the four blocks which were filled in 4th box.

According to this explanation, the 3 boxes in the bottom left corner and the one in the top right corner should be definitely filled.

And only box B satisfies this condition. So, done!!

I think B is the correct answer.

Explanation : Consider the following diagram and focus on the diagonal red lines. Actually boxes are filled in the order in which they appear in these lines. When all boxes in the last lines are filled then it starts again from top right.

A

The squares move in a pattern determined by the number of colored squares in a row. One purple square one move to the left , two squares two moves to the left… When the colored square moves off the left end it reappears on the right with an additional square added.

Here was my thought process…

Well each new grid adds an additional purple square, so you’re looking for an answer with 6 purple squares. That means F cannot be the right answer, leaving A, B, C, D, and E.

All of the grids are reflected across the diagonal line going from bottom left to top right. So that means D cannot be the right answer, leaving A, B, C, and E.

The 4th and 5th grids are the inverses of each other, which would lead me to believe the 3rd and 6th, 2nd and 7th, and 1st and 8th grids would also be the inverses of each other.

Which leads me to believe that B is the correct solution.

B because the squares gets filled sequencially

B is the correct answer to this question.

c