## 19 June 2011

### 55. Square 4X4 : How many Squares?

 Easy Medium Hard Extreme

How many squares in the figure? It looks easy, but make sure you count them all!

A total of 16 squares
1X1 squares : 9
2X2 squares : 5
3X3 squares : 1
4X4 squares : 1

1. Yeah cause show answer says so lol

2. there are 4

3. how'd you get that. I saw 16

1. What about the small squares the match heads and the ends make between the squares....

2. If you look close there isn't a 3x3 square. None of the sticks connect all the way across.

1. There is one

2. Bottom left is the 3X3

3. There is a 3x3

3. If you look close there isn't a 3x3 square. None of the sticks actually go across to make a 3x3 square.

1. Yes there is...you're just stupid

2. Don't call people stupid!

3. Stupid....

4. Start in the bottom left corner

5. Yes there are 16... Good observation!

4. when does a square turn into a rectangle? and does the L shape a real square shape?

1. a square is always a rectangle

5. Where is the 3 x 3?

1. Bottom left 3 up the side and 3 in right.

2. No a rectangle is not square it is it's defining characteristic and why it has a different name in the world of quadrangles

3. Start at the bottom left corner. 3x3 matchsticks, NOT squares.

6. i dont see how you can count rectangulars as squares..You are missing 4 matches to make up 16 squares...
can you explain that ???? thankssss

1. Look at the outer edges of the 2x2 etc that form squares in their own right.

2. OMG!!! Its matchsticks. Not squares. 4x4 matchsticks and 3x3 matchsticks. Lower left corner for the 3x3 matchsticks that make a square. And the 4x4 is the entire outside of the square. *sigh* smh

3. the mathsticks form squares........

7. There are only 8 actual squares.....

1. even if you only count 1x1 squares you'll get 9 but the answer is 16

8. There are also 2 of 1x2 squares which although most people call rectangles are still classed as a square

1. 1x2 s not a square it's a rectangle. All the ones counted where rectangles.

9. I've always thought the purpose of matches in a puzzle is the flexibility to move them around, without taking any away to come up with a finite answer. This is typically where people often get stuck thinking "inside the box", overlooking that matches are movable parts. This one is circulating on facebook, and if it was just about the squares, then why is it illustrated in matches instead of solid lines, I asked myself. Because matches can be moved to make more squares! My answer is 30! Thanks for indulging me!

1. sounds like you could be over thinking it a bit.

10. It is 19!

11. they need to be touching to be squares.

12. are you counting the squares where the sticks meat. If so then you are wrong. There would be 22

13. 15 or 0:

15...count big outer square first, then all the little ones inside (that's 10 so far), then the four quadrant squares that make up the big one, then the one in the middle made up by four little squares...

OR ZERO (NONE of the lines actually connect, so technically, these are just a bunch of segments that don't make any shape at all).

1. I think 0 also, since the sticks don't meet to form the right angle.

14. There is actually 17. I could 6 - 2x2's not just 5.

15. I count 17.

There are 6 2x2's!

1. I agree with you there are 6 2x2's but the answer doesn't agree with us, maybe they were wrong??

2. 2X2... think about it. 2 sticks on top and bottom, two sticks for either side... that makes 4 equal sides like you said. Squares.

3. Uh ok? I still have 16. Where are you getting 17. I got the 6 2x2 bit have no clue how you're coming up with 17

4. if you count 6 2x2s then it'd be 17 but explain to me where the sixth 2x2 is?

16. Yes there is...bottom left

17. There is NO square wherein there are 3 matches across all four sides, there is always one matchstick missing on one side. So there is no 3x3 in this puzzle.

18. OHP! I retract my last comment, I finally found the 3x3.

19. there is a 3x3 its the bottom left side 16 is the correct number

20. The 3 by 3 starts bottom left.

21. I got 19

22. Cody start in bottom left corner 3 x 3 :)

23. Try again Cody gofromthebottom left over 3 up 3.

24. The 3x3 square is on the lower left side of the puzzle.

25. The bottom left corner is a 3x3

26. Yes they do Cody... Start from bottom left.

27. What about the 17 square? Take off the top row & the right/vertical row. That leaves another large square...or would you argue that is a rectangle. It LOOKS like a square.

28. I saw 17 squares. If you remove the very top/horizontal row that leaves another large square...or would you argue that is a rectangle? It looks like a square to me.

1. "Argue" that is a rectangle? Wow.

29. Lower left corner is 3x3

30. Cody, yes there is. Start with the second row, go across three and down three, it's the only place it is possible.
xoxo

31. There is a 3x3 square, second row left + 3 then 3 down.

32. Cody, the bottom left corner is a 3x3 square, only the matchsticks outlining that square have to connect (not all within), so 16 is correct. There are nine 1x1's, five 2x2's, one 3x3, and one 4x4.

33. 3x3 is wrong... 3 matchsticks by 4 matchsticks do not make a square. The answer is 21.

34. Yes they do Cody, from bottom left - it goes up three and across three to the right, then down three and back across three to reconnect with the bottom left...

35. there is no 3x3 because you only have 3 on two sides of the lower left corner. There are no squares that have 3squares on each of the four sides to make a 3x3 square.

36. there is no 3x3 as there are only 2 sides with 3 smaller squares for the lower left hand corner and there are not 3 rows of 3 anywhere in the largest square. The lower left hand corner has an "L" that - if divided - would be 3 squares to make the 3x3. 15

37. Duh, there is one 3 x3 square, look closely- coming from the bottom left corner...

38. to Cody Adams there is a 3x3 square starting at the left bottom count three right three up three left three down, therefor a 3x3 square. the correct answer is 16 total squares. and to anonymous the match head are coned so they are not actually squares.

39. Bottom left corner, Cody.

40. Yes there is one 3 x 3 square. Start in the bottom left corner and count 3 sticks right or up and then keep turning & counting by three's to form the square.

41. 17 actually... you missd a 2x2 square.

1. Again!!!! Where is the 17 square?????

42. There is a 3x3 square, bottom left corner

43. Cody, look again. start at the bottom left corner, there is a 3x3.

44. @Cody, there is, on the lower right

45. I can't see a 3x3

46. Cody,
Starting from the bottom left corner go three over and the up. I had to turn the image sideways to see it.

47. Cody - Bottom left 3x3 quadrant.

48. There is a 3x3 square.
Start at the bottom left, 3up and 3 over. You'll see it.

49. Start bottom left corner and you will see the 3x3 square

50. @Cody Adams, bottom left corner is 3x3

51. If you look close they do connect buddy

52. yes there is a 3x3 from bottom left count up 3 accross 3 down 3 and back 3 and there is your 16th square

53. Where the heck did someone come up with 6 - 2x2's ?? There are only five. Four in each corner of the single large square, and a final 2x2 in the center.

If there were six, there would have to be one of four other spots splitting out from the center square in one of four directions here like this (+)

And yes, there IS a 3x3 for a total of 16 squares. However, to be argumentative - there is a final 17th square containing the square image. ;-)

54. I think I've lost all faith in humanity. The amount of people who can't see a 3x3 square, even after being told exactly where it is!, insane!. Theres only 4 possible places for one in this square so its not exactly a trick is it.

55. Where is this magical 6th 2x2 that people are talking about?

56. There IS A 3X3. Start in the lower left corner, count upwards 3 sticks, count across 3 sticks, count down 3 sticks, and across 3 sticks. This makes a square & you cannot deny that anyone.

57. the answer is 0 because none of the matchsticks are connected...i think

58. It can't be 0 because ALL of the match sticks are inside one outer square ;-) Either 1 or 15 depending on if you're counting the squares who's ends don't meet!

59. The answer above is correct. It is 16 squares and the 3x3 is found from the top count 3 small squares right to left and then up and down to find the 3x3.

60. Rectangles are not classified as squares. Squares are however rectangles. I count 15 actual squares. For a rectangle to be a square all the sides have to be the same length.

1. Square are not rectangles do you by chance mean quadrangles

61. Now I see the three by three. 16

62. And now for the real hardcore crowd....RECTANGLES!
6 2x1 Horizontal
6 1x2 Vertical
3 3x1 Hz
3 1x3 Vt
2 4x1 Hz
2 1x4 Vt
2 3x2 Hz
2 2x3 Vt
2 4x2 Hz
2 2x4 Vt
1 3x4 Hz
1 4x3 Vt
Grand Total = 32!!

63. I go with zero as well... By deff, no actual squares exist in this puzzle-

64. Whenver I wonder why I am doing so well in life even given the fact that I am quite lazy, all I need to do is look at comments of folks on this page and I know there are a bunch of morons out there.

There are 16 squares.
1x1 - 9
2x2 - 5 (not 6 like one tool wrote)
3x3 - 1
4x4 - 1

I cannot believe that folks in this discussion don't know the definition of a square like the person who decided if he took off the top row, a 4x3 was a square or the folks that asked if a rectangle is a square. I weep for our future.

1. Well now aren't you fortunate to be doing so well. I'm sure it's totally necessary for all of us perfectly moronic strangers to know such personal information...
Some people here may not be great with puzzles or even logic, but at least they aren't pompous or unnecessarily rude. Way to claim douchebag of the year!

2. Your answer is the best. I still don't understand how some people got six 2x2 squares but some couldn't find the 3x3 square.

65. There are also 7 tiny squares where the match heads meet. If those count then the total is 22.

66. Yay I got it right!!!!

67. I find 15... it says there is a 3x3 square and I can't find it.

1. 23. Where is the logic in THAT? With all the squares, I along with most everyone else, got 16. There is NOT 22 sqaures. Lol I would LOVE for you to prove me wrong and if you do, I will give you criedt publicly.

68. The 3x3 is bottom left

69. My brain doesn't work very well. Now I see the the 3 X 3 crap.

70. There are 16 total squares. To find the 3x3 square begin at the lower left corner. Count 3 matches along the bottom then count 3 matches up then count 3 matches along the top then count 3 matches down to the lower left corner where you started at. There's your 3x3 square.

1. Thank you. I was looking for ages and I couldn't see this one.

71. It's 16, end of.

72. A rectangle is square therefore if I counted correctly, there are 34 squares in the picture

1. A rectangle is not a square, which is why it's not called a square. A square has 4 EQUAL sides. A rectangle does not.

73. There are blatantly 16 squares. Also, It explains how many of each there are, so why are some people still saying different? 17? what are you on? there are only 5 2x2

74. There are blatantly 16 squares. Also, It explains how many of each there are, so why are some people still saying different? 17? what are you on? there are only 5 2x2

75. 16 Squares - Those who think that the its squares where the heads meet is I guess getting paranoid about the puzzle. The general idea here is to use the match stick length to make squares not its width. Secondly, there are people who are commenting on there are 0 squares for the same reason.

76. A Pure Science ZERO Squares- there are no right angles - the intersection of two perpendicular straight lines.

77. My answer is 10... The others r rectangle shape..its not square!!!

78. My answer is 10..the thre rest are triangle..!!

79. How about doubling all the lines since there are 2 equal sides on each supposedly match.

80. 16. 9 small squares, 6 medium and one big. The rest are rectangles. The matches don´t really touch, they just form shapes. This riddle is for logical and spatial thinking. It is made out of matches because it´s an old kind of riddle. People played it whenever they had time. Before TV.

1. 6 medium? I see 5 (4 outside corners & 1 center)
where's the 6th

2. 6 medium? I see 5 (4 outside corners & 1 center)
where's the 6th

81. There are 16

The 3x3 square is in the bottom left corner

82. The 17th square is the one framing the puzzle outside the question.

1. No. Thats the 16th squate. Count again. :)

83. How is a 2x2 and a 3x3 a square? Those are rectangles and irregular quadrilaterals, respectively.

1. Seriously? How is a rectange with 2 matches on all four sides (which is what people mean by 2x2) not a square?

2. Omg anonymous you nailed it! A square has 4 equal sides. Meaning 2x2. So all four sides have 2 matchsticks, 1 matchstick, or 4 matchsticks. A rectangle has 4 side. 2 equal longer length sides and 2 equal shorter length side. Smh. I would LOVE to know where people learned their basic geometry.

84. Time to square off on this and get everything squared away ;P

6 - there are 36 matches, therefore the picture contains 6 perfect square roots: 1(2), 2(2), 3(2), 4(2), 5(2), 6(2)
6 - the picture contains 5 Carpenter Squares and 1 T Square.
16 - 1×4×4, 1×9×9, 5×2×2, 9×1×1
25 - A rectangle of infantry was referred to as a square, historically.
48 - if you lay two pieces of wood that are straight and parallel to each other they are said to be square. There are 48 parallels.
164 - 2 consecutive 90 degree angles, such as on a board, is said to be square.

Everything I listed falls into the definition of square in the dictionary.
The total is 265

1. No proof the matches aren't round

85. Square is a smoke(urban dictionary). There are 36 match sticks.1 match stick per square = 36 squares

86. I come up with 23, if you count the squares formed by 4 matches meet