How many squares?

Howmanysquaresgrid.jpgFor something lighter this week, our daughter presented me this grid of squares with the comment, “Layout is all about visualizing, right? This looks like a good exercise for that.” And I’m like, okay, I think you’re right. Layout handles both real and phantom interactions between objects, shapes, colors, and other elements in a structure, in positive and negative spaces. The better you can visualize the interactions, the better your designs will be. So the question is, how many squares do you see? Answer next post.



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150 Responses to How many squares?

  1. TImBo says:

    39-ish.

  2. Nikola says:

    Ali Baba and the . . . squares :-)

  3. Kim Kenyon says:

    I found 40, but that’s before my morning coffee. Are there more? I love to use grids in my designs, both visible and invisible.

  4. Craig says:

    I see 36 squares.

  5. Per-Ulf Allmo says:

    39 squares

  6. Judy Robertson says:

    39

  7. Max says:

    I’m seeing 29.

  8. Andrew says:

    This has been doing the rounds on social media for a while now. Funnily enough, I was looking at it before tea. Although it’s not quite my forté, I was wondering about using it at an away day for team-building, although I fear sane team members may crack up over it. Still, I’ll leave it for teasers to spoil the surprise, unless the four English and one German clues I’ve just dropped are enough . . . ;-)

  9. Alan Kirk Gray says:

    Not sure how many I see, but I think there are 38 as it’s laid out.

  10. Ron Bruner says:

    There are at least 36 squares that can be constructed from the lines shown; more are possible if one imagines the extension of lines that terminate within the field.

  11. Andrew Porter says:

    If we’re meant to answer, my answer is 40.

  12. Mike B. says:

    40 including the grey lines . . . 9 of the black lines only

  13. Linda says:

    That’s just mean. I found 41 but may have missed some.

    • Lezley says:

      How did you get 41?

      • Amy says:

        Actually, I counted again and got 50. You need to count all separate small boxes, all medium, the large, the sum of each and the ones that are like the outlined one in the lower left.

  14. Donna says:

    29 squares.

  15. Scott M says:

    34

  16. Marie Gale says:

    Feels a little like the site I’m working on right now! 36.

  17. Beth Redmond Walsh says:

    I got up to 40, and after realizing that the dark outlined squares are hints for seeing other potential ways to view more squares, I thought maybe I should count them again!

  18. Inês Faël says:

    Hello John,

    Does the answer include all the squares or just the black ones? I count 9 black squares and 29 grey+black squares.

  19. John Driscoll says:

    Do you mean how many BLACK squares do you see? I see 9.

  20. Inês Faël says:

    Actually, no, there are more black+grey squares. Counting all the combinations, there are 43 squares.

    Did I miss any? :-)

  21. Kelly Weston says:

    I see 30 squares . . .

  22. Len Williams says:

    29 squares, which includes all interactions between black and grey lines and the overall square outline of the shape.

  23. debora says:

    The first time I did this I counted 40 squares — hasn’t changed since.

  24. Leona says:

    This a really fun exercise. I counted 30 squares.

  25. Brian Whalen says:

    I think I counted 9 squares. It’s an interesting exercise, for sure.

  26. Amy says:

    I’m getting 49.

  27. Larry says:

    I’m going to say 40

  28. susan says:

    I think if you have over 40 squares, you should link to your sketches here. I would love to know!

  29. serdar gencer says:

    I see 40. I didn’t split the lines with grey or black ones. I see 40 squares there :-)

  30. Christina Vasilevski says:

    I see 42. Let’s just assume that it’s a friendly little sign from the ghost of Douglas Adams.

  31. Roberta says:

    I see 39 squares.

  32. 40.

    I shared this on my Facebook page awhile ago and everyone loves counting ‘em — it has been my most popular post!

  33. Mats (from Germany) says:

    Grey and black lines = 40
    Black lines only (no grey lines) = 9
    Grey only (no black lines) = 1

    So, the real equation is:
    40 + 9 + 1 = 42
    ;-)

    • Rebecca says:

      Um, on earth, 40 + 9 + 1 = 50, not 42. Plus, I don’t see any grey square only (no black lines). Very confusing.

  34. Paul says:

    Great exercise. I counted 40 squares.

  35. Burak says:

    40 sounds right to me as well.

  36. John M says:

    I counted about 40 too.

  37. Karen says:

    At first I saw, 27. Now I get 35, but the comments indicate there are more. Maybe a little lunch will trigger a different response.

  38. Karen says:

    Oops, make that 39.

  39. Carol says:

    Hi John,

    I see 40 squares. I love visual puzzles! Actually, I love all types of puzzles . . . Andrew’s post is quite clever. Design, for me, is like solving all types of puzzles such as visual, word play, logic, lateral thinking, and of course jigsaw puzzles.

  40. Nick says:

    I count 41. How many did I miss?

  41. Jim says:

    40

    See animated count at http://goo.gl/2AtrP

  42. jd says:

    40

    1/2 x 1/2 squares = 8
    1×1 squares = 18
    2×2 squares = 9
    3×3 squares = 4
    4×4 square = 1

    • Heather says:

      Thanks! I could only see 36 until you posted this breakdown — then I realized which four 2x2s I’d missed.

  43. Tricia says:

    30 squares altogether, overall, I think.

  44. Hernâni Barros says:

    I count 36 black and grey squares. 9 if I consider only the black squares .

  45. Marjorie Hanson says:

    I counted 50

  46. Blaine says:

    9 in black, 34 in gray, 40 unique when combined . . . I think :-D

  47. cattcatt says:

    I stopped counting after 33 with the gray boxes . . . attention deficit. Most comfortable with the dark lines and the clean rows of boxes. Started getting annoying after realizing the gray boxes can be grouped together for more boxes.

  48. Carl says:

    40 me thinks

  49. Nico Bouwman says:

    I count 40 squares — nice puzzle!

  50. Brendak says:

    I found 40 including gray and black lines . . .

  51. Joan says:

    39, but not adamant about it

    • Laurel says:

      I thought 39, but my partner mentioned the overall outline is also a square, so I think it’s 40.

  52. jskbydesign says:

    30 are drawn or showing. If changing the drawing and adding to — the number will go up.

  53. Eric says:

    Also 40

  54. Dawmn says:

    I have 38.

  55. Christina says:

    I think there are 42.

  56. Rachael says:

    39, but I may have miscounted, so maybe 40. 40 is my final answer. I thought the 2 x 2 gray square in the middle was the sneakiest. Do we win a prize for getting it right? :-)

  57. Ted J says:

    Four-tay

  58. ana gonçalves says:

    I see 30 squares.

  59. Vincent Rios says:

    Are you removing the grid from this question?

    If yes, Then I see 9 “squares.”

    I you want to count the whole display area, then 10, which would have been my answer unless . . .

    If you want to count the grid, add 25 to get 35.

    If you want to count the grid interactions with the black objects, add then add 5 more for 40.

  60. Tammy says:

    I got 43! :-\

  61. kmc says:

    I see 4 total . . . one large, one medium, and two small.

  62. Rik McRae says:

    I count 41 . . . unless it’s a trick and some of them aren’t square!

  63. Rik McRae says:

    No, I take that back . . . 40!

  64. Frank says:

    I got 40 as well.

  65. Mary Ragland says:

    41?

  66. Roz says:

    By my count, 40!

  67. PStigerID says:

    160,262 squares . . . zoomed in to count all the pixels :-P

  68. Paul V says:

    I see and count 40.

  69. EZIO MATTASSI says:

    I see 38 squares.

    • Claire says:

      Did you count the two squares forming the borders around the mini squares that are off-grid?

  70. sneed says:

    I continue to get 29 and am really curious about how others are seeing more than that.

  71. Tommy V says:

    There are 9 using only the black lines, and 40 if you use all of them.

  72. Glynne says:

    40. Had to look a number of times and kept seeing more. Those little ones got me!

  73. Marie says:

    Huh. I only see 29.

  74. Lori Rigden says:

    43

  75. Lezley says:

    Designed like quilt blocks using all renditions of square, square in square, I found 40 — and then designed a quilt!

  76. Maiyo says:

    I got 40 . . .

    16 * 1×1
    09 * 2×2
    04 * 3×3
    01 * 4×4
    10 * mini 4×4

  77. Becca says:

    At first glance, I “see” four.

    If I actually count, I find 40.

  78. Robert Cayer says:

    I got 41.

  79. Victor says:

    “So the question is, how many squares do you see?”

    Well, on first glance I see 4 accented squares. I did not count them.

  80. Ambrose says:

    I’ve seen this on Facebook some time ago. I counted 40 too.

  81. Paul says:

    Six.

    I can see more, but my brain is weary to count them all.

    The number of squares I feel is about 6.

    The two large ones . . .

    Their intersections . . .

    The two smaller, central ones . . .

    and it’s all held together by the large boundary square. (optional)

    I could add more detail, but I guess the exercise is about perception, and my eyes tend to ignore the grey squares as unimportant and see the blacks as more so. The interaction of squares also creates a “tension” that makes them stand out.

  82. Michael Weckert says:

    Hey all,

    I come up to 34.

    Greetings, Michael

  83. I got 40 as well. I was going to say 39, but I almost forgot to include the large square on the outer border.

  84. Wallace says:

    I found 42 . . . answer to life, right? ;-)

  85. Rystraum Gamonez says:

    Wait ’til you ask, “how many rectangles are there?” and see people tripping over the squares-are-rectangles argument.

  86. don says:

    I count at least 66, including imaginary squares missing one or two lines. It is difficult at first and depends on the rules applied.

  87. jean quintella says:

    37?

  88. Toshko Postalkov says:

    Black line squares are nine. If we add the grid lines, the total is 57 squares. Don’t forget the grid squares forming at the middle. But since this is not an applied math forum, I think we are missing the point of the question here. From subjective point of view all answers are correct, because to you as a viewer all that matters is how many squares can YOU see.

  89. Sunanda says:

    At first glance I saw only 4 with black outline. After a while I noticed the intersection of two big squares forming the 5th square same size as the small ones.

  90. Gaurav says:

    To me, that is a 16-square grid, but it can be a 64-square grid with the underlying half-square grid. In fact, a 64-square grid would make the layouts interesting.

  91. Lynne adams says:

    First time I counted I got 25. Then recounted and got 42.

  92. Beth says:

    I get 40 squares. I get a lot more rectangles, but I don’t see 54 squares.

  93. LoriC says:

    I admit I went a little square crazy — way beyond those outlined in black and gray. I envisioned a lot more than what is actually there.

    In my mind’s eye, I could see squares within squares within squares within squares within squares . . . until they got too small for me to see or count. Color markers helped. But I stopped “seeing” at 1,378.

    A fun exercise. ;~)

  94. Dan says:

    There are 40* squares if you ignore the color (black/gray), but is there a more subtle punchline to this question? :-)

    Is it square to just sum up the squares?

    * 4^2 + 3^2 + 2^2 + 1^2 + 2 + 8 = 40

  95. Hasse Rasmussen says:

    If the question is: How many squares do you see? It doesn’t matter what colour they are. In that case I count 40 squares.

    You need to have eyes for the initial question, otherwise you can get sidetracked.

  96. Lezley says:

    Still can’t see more than 40 and certainly not 50+. Perhaps the definition of SQUARE is coming into question? “Square” as in four EVEN-sided elements?

    • Chloe says:

      LOL! All those counting over 40 are seriously over-counting or doing something wrong — there are only 40!

  97. RIch Martin says:

    You asked how many squares we see. All totaled, light grey and black, I see 30 SQUARES, of them 9 black squares.

  98. rowen says:

    I see 44 . . . :-)

  99. Cathy says:

    29 — easiest to see

    95 — imagining all the subdivisions using the smallest outlined square

    Oh, but now I’m thinking about a few more combinations, or did I count those already? I’ve lost track, again!

  100. Sherri Rannells says:

    I see 40 squares.

  101. Bagher says:

    A fair 44

  102. Bagher says:

    And the winner is 48.

  103. Bagher says:

    . . . or all are losers, and 40 is the winner.

  104. Debbie Lind says:

    It’s looking beyond the obvious. With each square being counted, I said, oh yes, another one I didn’t see. This is a great “eye training” exercise.

  105. snipyto says:

    There are actually 22.

  106. Kashif says:

    Eighteen

  107. Ananta says:

    If see this riddle in another way, in terms of emphasis then there are 8 squares. Other squares are not meant to be counted I reckon :-)

  108. Jamie says:

    There are a total of 30 squares in a 4 x 4 grid.

    1 by 1 = 16. 4 x 4 = 16
    2 by 2 = 9. 3 x 3 = 9
    3 by 3 = 4. 2 x 2 = 4
    4 x 4 = 1. 1 x 1 = 1

    Plus the two small boxes and the sub boxes of those = 40 then subtract the 8 boxes that the two bold black boxes interrupt. = 32

  109. Dave says:

    I got 44 after confirming four times.

Comments are closed.