Shapes and Patterns 3 – Tic Tac Toe?

Algebra Level 1

Which of the following best completes the pattern above?

A B C D

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69 solutions

Revant Chopra
Jun 8, 2014

No real pattern really. The second square was the only one remaining out of 9. Any other solutions?

There are several patterns involved in this.

For example, if you focus on just 1 row (column) of 3 × 3 3 \times 3 squares, you will see that there is exactly 1 red square in each row and column.

There is also another pattern that is related to magic squares.

Calvin Lin Staff - 7 years ago

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Its a S alphabet see through half open half closed eye

Yash Jaiman - 5 years, 10 months ago

Hey yeah! Should've seen that. What's this about magic squares you say? Di tell.

Revant Chopra - 7 years ago

I think the pattern looks like 'S' and we just had to complete it by analysing the symmetry.

Brijesh Shukla - 6 years, 11 months ago

That was my way of thinking also.

Queen Elizabeth - 5 years, 11 months ago

Only box ot covered

Lalit Akhade - 6 years, 11 months ago

No Solutions Needed All Of Them Is Covered But In Different Boxes But Only One is Not

Lenard Arceo - 6 years, 11 months ago

there IS a pattern: look at the corners, and then the edges!

Matthew Hayes - 5 years, 9 months ago

There are several patterns involved in this.For example, if you focus in column 1 of the square by 3, you will see that in any square there has exactly 1red square in each row and column

Joel Vega - 6 years, 11 months ago

The answer was easy, but they put the answer letters in an order that was not alphabetical. So, in an attempt to be quick I accidentally chose "b" which was in the "d" position.

Derek Wheeler - 6 years ago

Chess players will get this: 1st-2nd box was an L-move (knight move in chess). Same with 2nd-3rd. Then the shade moved one square up (3rd to 4th) (queen or rook move). Then 4th-6th move was 2 squares diagonal (one per move) (bishop move). Then one square up again (7th) then knight move (8th) so it should be letter D.

i thought the same, i'm happy to see that there is at least one guy in this world who think like me. :D

Akshay Nagraj - 6 years, 9 months ago

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I am also there. I thought the same way

Anubhav Sharma - 6 years, 1 month ago

That's how I got the answer.

David Carlson - 6 years, 2 months ago

you mean 'bishop' not rook

Jacob Case - 6 years, 10 months ago
David Bass
Jun 26, 2014

The solution is D, which is the only square not already represented in the 8 boards.

Absolutely brilliant David. :D

Finn Hulse - 6 years, 11 months ago
Paolo De Angelis
Jul 26, 2014

the sum of each row/column/diag. must be 15 - magic square - (counting red square from left top 1 -to bottom right 9) so...

Vishnu Tilak
Jan 5, 2015

it is in a matrix form 8 1 6 3 5 7 4 9 2
it is a brilliant order having sum 15 if we add any three numbers in a row or column or diagonally so the answer is 2

Rajaa Sahil
Jun 23, 2014

Simply see the diagonal.

Yes its the diagonal

Adnan Gulegulzar - 6 years, 11 months ago
Aayushi Arya
Jun 30, 2014

See the no. of the colored box. first-8 second-1 third-6 fourth-3 fifth-5 sixth-7 seventh-4 eighth-9 ninth-????? Add 8+3+4=15
1+5+9=15 thus,6+7+x=15 x=2 THUS THE ANSWER IS D

exactly how i got the answer...but i am sure there r other ways how it can be solved since it is a problem on shapes and patterns....pattern recognition...

Alde Hill - 6 years, 10 months ago

D would be right Answer in 1st row of boxes In box 3 2 1 are red in 2nd row of boxes In box 1 2 3 are red so in 3rd row 2 3 1 must be red.

Sahil Kalra - 5 years, 9 months ago

Think simple....

Harikrishnan Raju - 4 years, 7 months ago
Sanjay Kumar
Jun 29, 2014

the first shows every 3 3's row is shaded similarly the second row ,coming to the third row the missing one should be a 3 3 with first row shaded

Eduardo Maçan
Jun 10, 2014

It's all about turning things clockwise. Start from the top left corner, for instance. In order to get the pattern in the next clockwise position just take the current pattern, turn it clockwise and then move the red square clockwise inside the pattern.

Ryesah Amerol
May 25, 2015

Hey you can try crossing the red boxes , just like sudoku. You'll get me eventually.

Iuki Nishikawa
Jun 25, 2014

An interval of 4 boxes that are not shaded.

Harikrishnan Raju
Nov 13, 2016

The solution is that the opposite cubes are twisted 180 degree clockwise. So the missing cube should be obtained by twisting the first cubes 180 degree clock wise .

Sagiv Mor
Aug 27, 2016

looking only on the left row, the red square went 3 steps across the big square. first to second - down left left. second to third - up up right.

I just did the reverse of the first row.

Shantanu Rahman
Nov 9, 2015

I think it is more about chess moves. first one was knight move. next diagonal move. third came out to be another knight move.

Champ Luci Fer
Nov 5, 2015

Follow the path as a Knight travels in chess. And bravo !

Priya Pancholi
Oct 24, 2015

Suduko style.

Deepa Ramesh
Oct 11, 2015

It moves like how a knight moves on a chess board

Jamie Eberling
Oct 9, 2015

Just look at it like a game of sudoku.

Phil Lip
Oct 9, 2015

I'm unsure about a concrete solution, but there are at least two ways of seeing the answer. The blocks go in a pattern like the knight on a chess table counterclockwise around the outer grids and then the middle one just happens to have one in the middle.

Also, and this is very unsatisying, the option D is the only one that isn't already there.

Halp pls

Biraj Kundu
Oct 5, 2015

Simply follow the pattern In column 1 the red dot moves 1 space right and 1 space up similarly in column 2 and 3 You will find the right option

Mishail Singh
Sep 26, 2015

The pattern of similar to the house move in chess.

Ryan Trebilcock
Sep 10, 2015

I went by analyzing the middle block. Each red square is in the opposite position than the block on the other side of the middle.

Drew Davis
Sep 9, 2015

I thought of it this way: in relation to the center block, the blocks on opposite sides of are flipped. Look at the top middle and bottom middle, then top right and bottom left, and so on. So if you flip the image of the top left block you get your answer.

Yassine Alfa
Sep 8, 2015

It's like suduko

NelJorn Aguas
Sep 7, 2015

I just thought its the inverted 1st column

Actually I got a pattern on this. I don't think if I just luckily guessed the correct answer or the pattern I thought was effective. haha 1. Starting from the first box, move three squares on the edge clockwise. It will lead you to the second box. (the one at the right of the first box) 2. Then move again three squares on the edge clockwise. 3. Then do it for the third time. (it will lead you to the box at bottom of the third box) 4. After the red square completed one revolution on the edges, it moved diagonally to the center. 5. Then again moved diagonally towards the corner. 6. Now move three squares on the edges counterclockwise. 7. Lastly, moving three squares on the edges counterclockwise will lead you to the last box. 8. And doing the same procedure will fill in the missing box.

I know it's weird and time-wasting procedure because the given boxes can give us clue about the remaining spot where the red square didn't land on, but it is quite a challenge for me to know/create a pattern and the arrangement of the boxes helped me to do that. PS: please pardon me for the long explanation/comment. It's my first time posting my own observations here. Please bear with me. :)

A Macd
Sep 3, 2015

I noticed there were two closed cycles and a third cycle which was left open by the missing square, D completed it.

e.g. the middle square sends you back to itself. The top right send you to the middle right, the to the bottom left, middle left then back to the top right.

The open loop starts top left, mapped to bottom middle then to the missing square which with D maps you back to the top left.

Probably just a happy accident but it got me the right answer.

Robson Costa
Sep 3, 2015

didn t have the image d

Shekhar Chaudhary
Aug 31, 2015

Its d S pattern n only box left uncoloured

Shankha Das
Aug 30, 2015

following the pattern its going to skip 2 next then take a position

Chris White
Aug 28, 2015

Just used process of elimination since none repeated themselves and only D was left.

Jian Yi Lee
Aug 28, 2015

Just do it the SUDOKU way

Rahul Mohta
Aug 22, 2015

Answer is d bcos it is opposite to the first 1

Chuck Batcheller
Aug 21, 2015

If you think of it as rows numbered (1,2,3) ; (4,5,6) ; (7,8,9) you'll notice that it is rotating from a non corner number (2,4,5,6,8) to a corner number (1,3,7,9) every other move. Therefore, the last move is to the last remaining corner.

Shivam Sabharwal
Aug 21, 2015

There are two patterns...occuring alternately... In one corners are being marked.. In the other the other pieces.

Cullin Bv
Aug 17, 2015

I looked at it the hard way... the pattern I first noticed was the middle on was to be ignored and the pattern was just looking at the remaining 8 as 2 separate but still relatable problems. The 3,4,6,7 red squares are are clockwise as to where they should be and 1,2,8,9 are counterclockwise as to where they should be.

It would definitely help if I had a picture because I feel as though I explained it awkwardly.

Anthony Kupecz
Aug 14, 2015

Analyzing from top to bottom, you notice that the square moves down a row and over one column (taking into account that once you get to the bottom of the square, it starts back up to the top of the square). For example, in the first column, it is on the third row, second column. Then the next one should be on the top row (since there is no fourth row), and the third column. Applying this observation, to the third column group of squares, you find your answer.

Omkaar Mishra
Aug 9, 2015

The other squares as a whole forms the letter S. So we just need to choose the opposite position of the first square .

Smiley Jayee
Aug 7, 2015

I just did the tic tac toe and put x or o according to the red squares one by one and gt the ans.

consider (a,b) where a=nth row, b=mth row then it is of pattern (3,2) (1,1) (2,3) (1,3) (2,2) (3,1) (2,1) (3,3) (1,2)

M Marathe
Aug 1, 2015

Going from top left grid down and around the central figure anticlockwise, you see the red square moves by one square, anticlockwise around the rim and then the whole grid is rotated a quarter turn anticlockwise. This is one transformation. Continue doing one transformation per grid going around the whole figure. The central figure doesn't fit this pattern though. One could say it completes the whole thing by filling the only square that wasn't filled in any of the others.

Iury Bessa
Jul 16, 2015

If you play sudoku enough you will see the pattern quickly. Take the first row of 3x3 boxes and see that each red box is on a row independently from the others. Now take the first column of 3x3 boxes and notices that the red boxes don't overlap with each other for the individual columns. To find the missing 3x3 box do the same thing with the right most column and the lowest row to find the missing 3x3 box.

816 357 49? Add any row or column sum=15 The numbers are the boxes which are colores

Tony Anzalone
Jul 2, 2015

If you imagine that once leaving the grid you appear on the grid below. Now understand that there are 3 sets of 3 grids and the pattern progression is read grid to grid downward and not left to right. If you then look at the first grid and move down one square and then one to the right you have the second red square in the second grid. Then move down one and one to the right again and you have the third red square on the third grid. The same holds true on the next set of grids. Down one and one to the right and you are in the center square down one and one to the right and you have the right corner square. The trick is to imagine that once you leave the grid your imaginary red square moves to the grid below it. Easy to see but hard to explain.

Austin Hunter
Jun 22, 2015

it was simple I'd just looking for the missing pattern

Naveen Pandey
Jun 21, 2015

This was quite predictive as the only box which was not colored in the above eight pictures was the answer but to deal with such patterns have a look at my solution.

Consider the box to be surrounded by other boxes, you'll notice a diagonal (downwards-left) motion of the color.

Mohit Tekriwal
Jun 3, 2015

just look at the sum of the coordinates of the coloured boxes. then sum the sum of the coordinates in columns . you will find the sum in each column to be 12 hence 3 fits the pattern

Vagu Vagdhevi
May 25, 2015

apart from D rest of all are there in the question. so i thougt D as answer

Abdullah Masood
May 21, 2015

its an good but just a miner game of kid

Héctor González
May 21, 2015

Each matrix has a red square that indicates the matrix which has it's red square in the opposite end of the matrix mentioned at the beginning. Note that matrix [1,1] ([x,y], 1 being left in "x" and top in "y") has it's red square at (2,3), and matrix [2,3] has it's red square at (3,3), which is the opposite end of matrix [1,1].

Arun Chaudhary
May 10, 2015

Just like Sudoku

Adrian Cookson
Apr 22, 2015

Up two, left one. Simple.

Ashutosh Verma
Mar 21, 2015

see only middle diagonal boxes you will get answer

David Wang
Jan 10, 2015

I've been reading through the solutions posted here, but I never did see the one that I came up with, which i think is probably the simplest; If you look on the left side of the set, you can take the 4 squares(3 on the left side and then the one in the top middle) and then reflect it on the other side of the middle square(or rotated it 180 degrees) then you have an exact image, just missing the one block in the corner, so it would just be the block in the top left flipped upside-down.

There are nine squares of which the one not shown in the illustration is the alternative that appears in "D".

Only option D has not been used in the pattern. Thus, it is D. But what I actually thought was if you combine a row or a column there should be one red square in a row and in a column.

Edwin Cordova
Sep 24, 2014

all lines and columns sum 15 according to the position of the square (magic squares) If you have played sudoku the answer would be really easy. Other pattern recognized is every line horizontal and vertical have a red square on each line and column,

Sahil Nare
Aug 31, 2014

See the diagonals and you will get the answer.

Mylene Orbase
Aug 29, 2014

Left down.

Jack Mamati
Aug 14, 2014

The red shade moves 2 squares right diagonally up. If it reached the top/right most part, it should move next to the bottom/left most part of the 3x3 square.

Ozan Leylek
Aug 4, 2014

Oh well I saw that red squares goes to an edge than another square is cross up or downof the previous square presented in thencolumn so , logicaly D was fit as there werent the red square pattern that is up , cross to 1 st square in 3 rd column , simple . But inevidably , wrong

Peter Lee
Aug 2, 2014

this is a knights square, a knight moves in an L pattern

a knight moves so that it goes 2 blocks in one direction, then 1 block parellel to it.

Peter Lee - 6 years, 10 months ago
Cibi Sounder
Jul 15, 2014

There is actually a pattern. In the first four boxes , the red dot is displaced in a fourth box from its previous position,including the box from which it moves. In the next four boxes , the red dot is displaced in a 5th box from its previous position. Thus the next dot must be in a 6th box from its previous.

Benjamin Duron
Jul 9, 2014

The first 4 shapes rotate clockwise 1 time (90°) + move the dot by 1 case to the right (relative to the center).

The 5th shape (dot at the center) resets the rotation.

The 4 last shapes rotate counter clockwise 1 time (90°) + move the by 1 case to the left (relative to the center of the shape).

So the last shape is D.

Tsuna Quintil
Jul 6, 2014

From the first and second given example shown above the third example, you can clearly see that all the dots were placed winningly against the opponent. In order for the problem to be solved, the 1st player should pick what could be his best move. The best move was D.

Naufal Pramono
Jun 25, 2014

The pattern is D. Why? Because can you see the third pattern is in different position but the is same. So, the answer is D

Ramji Varadarajan
Jun 12, 2014

The first four images corresponds to the next four(excluding the fifth image with red dot in the center) as we compare 4th image with 6th, 3rd with 7th and 2nd with 8th respectively.

We can observe that they are exactly opposite to each other .

this is the only one left out shaded

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