Count the Squares 1

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There is a count the squares puzzle that seems to be running rampant on the internet.

Here is the picture and the words that go with the puzzle.

PLEASE HELP! I just got into a heated battle with Don (our boss) over this – I got 24 squares, he says 25. How many squares do you see!!?? -Nudge

I decided to answer this silly puzzle once and for all. I’ll post the answer in the comment.

I don’t know what the political implications of this are.

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One thought on “Count the Squares”

  • SteveG Post author

    Number the atoms so as to describe the makeup of the 40 squares.

    Now assemble the puzzle by overlaying the red squares over the
    black squares and count the squares.

    Red atoms
    in 1 x 1 arrays

    1. Atom 1
    2. Atom 2
    3. Atom 3
    4. Atom 4
    5. Atom 5
    6. Atom 6
    7. Atom 7
    8. Atom 8

    Black atoms
    in 1 x 1 arrays

    1. Atom 9
    2. Atom 10
    3. Atom 11
    4. Atom 12
    5. Atom 13
    6. Atom 14
    7. Atom 15
    8. Atom 16
    9. Atom 17
    10. Atom 18
    11. Atom 19
    12. Atom 20
    13. Atom 21
    14. Atom 22
    15. Atom 23
    16. Atom 24

    Red atoms in
    2 x 2 arrays

    1. Atoms 1, 2, 3, 4
    2. Atoms 5, 6, 7, 8

    Black atoms in
    2 x 2 arrays

    1. Atoms 9, 10, 13, 14
    2. Atoms 10, 11, 14, 15
    3. Atoms 11, 12, 15, 16
    4. Atoms 13, 14, 17, 18
    5. Atoms 14, 15, 18, 19
    6. Atoms 15, 16, 19, 20
    7. Atoms 17, 18, 21, 22
    8. Atoms 18, 19, 22, 23
    9. Atoms 19, 20, 23, 24

    Black atoms in 3 x 3 arrays

    1. Atoms 9, 10, 11, 13, 14, 15, 17, 18, 19
    2. Atoms 10, 11, 12, 14, 15, 16, 18, 19, 20
    3. Atoms 13, 14, 15, 17, 18, 19. 21. 22. 23
    4. Atoms 14, 15, 16, 18, 19, 20, 22, 23, 24

    Black atoms in 4 x 4 arrays

    1. Atoms 9, 10, 11, 12, 13, 14, 15, 16,
      17, 18, 19, 20, 21, 22, 23, 24

    I believe this is a rigorous enumeration of all the possible 40 squares. If you can come up with more than this, please tell me how.