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  2. 3-color cube

  3. Twenty Questions

    I did not see this puzzle mentioned in the forum before: Twenty Questions by Don Woods. I was able to solve it by computer (I verified my answer with the author), but even that wasn't easy! I'd love to hear of others' experiences with it. ^.^
  4. Yesterday
  5. 3-color cube

    This is a good point. I should clarify that for my answer, I assumed that if one configuration of colors can be transformed into another by rotating the cube, then they should not be counted as two distinct configurations.
  6. 3-color cube

    I'll just point out the interesting fact that with a tetrahedron, saying "two sides white" exhausts all permutations, since all pairs of sides share an edge. But with the cube this is not the case. So, I'm wondering what "patterns" is intended to mean: combinations? or permutations?
  7. How many squares?

    Best answer so far. Can you do exactly one (1) better?. Touching refers to red squares, which do not touch: Every point in the plane belongs to at most one red square. Donald Cartmill: Can you do exactly one (1) better?.
  8. 3-color cube

    I think...
  9. 3-color cube

  10. 3-color cube

  11. How many squares?

    Tried to edit my previous answer and lost everything . Correction ...Red sq "beneath "gray and rotated 60 degrees; Red sq "a top" gray sq and rotated 30 degrees new answer is 8 ; 1 beneath the gray but rotated 60 degrees ,a 2nd above the gray but rotated 30 degrees.4 more one at each corner= 6 ,however if you rotate the top two corner reds away from center you can place a red with one corner touching the gray at the mid point of the top side of the gray. You can do the same at the bottom two corner "Reds",rotating them outward and then placing the 8th red with a corner touching the gray at the midpoint of the grays' bottom side. If the red over gray is considered to be touching the red beneath the gray then the answer is 7
  12. How many squares?

    Captain Ed had the answer a red beneath the gray but rotated 60 degrees; another red a top of gray and rotated 30 degrees. Then you have one red at each of the four corners,which totals 6 new answer is 8 ; 1 beneath the gray but rotated 60 degrees ,a 2nd beneath the gray but rotated 30 degrees.4 more one at each corner= 6 ,however if you rotate the top two corner reds away from center you can place a red with one corner touching the gray at the mid point of the top side of the gray. You can do the same at the bottom two corner "Reds",rotating them outward and then placing the 8th red with a corner touching the gray at the midpoint of the grays' bottom side. If the red over gray is considered to be touching the red beneath the gray then the answer is 7
  13. Last week
  14. How many squares?

    how are we defining touching?
  15. 3-color cube

    I got
  16. How many squares?

    How about
  17. How many squares?

    More red squares can be overlapped.
  18. How many squares?

    Gray squares overlap red squares but the overlap need not involve a corner (e.g. aligned centers and rotated 45 degrees.) Overlap can be any positive amount, from full overlap to a small portion of a corner, but positive - not zero. And of course there is no Red/Red overlap; red squares do not touch.
  19. 3-color cube

    If each side of a tetrahedron is an equilateral triangle painted white or black, five distinct color patterns are possible: (1) all sides white, (2) all black, (3) just one side white and the rest black, (4) just one side black and the rest white, and (5) two sides white, while the other two are black. If each side of a cube is painted red or blue or yellow, how many distinct color patterns are possible?
  20. How many squares?

    Assuming the gray square can only touch each red square corner-to-corner or corner-to-edge, my answer is ...
  21. How many squares?

    Dang, I blew my spoiler again...I’ll be back. I’ve got an answer...sigh
  22. How many squares?

    “Touch” elucidation question: Does the gray square overlap red squares? Or can only edges overlap? Or can they only share single points?
  23. How much white?

  24. How much white?

    The area of the triangle is 1. What is the area of the white portion?
  25. How many squares?

    I randomly drew some squares on a sheet of paper and colored them red. Then I drew a gray square of equal size and counted the number of red squares it touched. Not very many. I forget the actual number, might have been 4 or 5. But it made me wonder: What is the largest number of red squares that a single gray square can touch? The squares are all of equal size and none of the red squares touch each other.
  26. Earlier
  27. Suppose you have a point within a equilateral triangle. If you were to connect each vertex to this point you would make three new line segments. Assume that you knew two of the angles formed at the point. Build a triangle out of these line segments. What can the two known angles tell us about the angles of this newly created triangle.
  28. Finding a function

  29. Finding a function

    Sort of combining the two solutions already given
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