BMAD

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About BMAD

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  1. Suppose we have two congruent equilateral triangles with side length of 8ft. They are on top of each other in the same orientation. Now One triangle is rotated by 180 degrees and is laying on top the other triangle forming a star. The triangles are positioned relative to each other such that the distance from the base of one triangle is 6ft to the base of the other triangle. What is the area of the star?
  2. Assume an exclusive OR.
  3. Why can't a right triangle with an hypotenuse of sqrt(24) have an area of 13 squared inches?
  4. There is an equilateral pentacontagon (a polygon with 50 sides). In one of its vertex stands Dr. Faust. He has three options 1) walk to the diametrically opposed point free of charge; 2) walk counterclockwise to the neighboring vertex by paying $1.05 to Mephistopheles; 3) walk clockwise to the neighboring vertex by receiving a payment of $1.05 from Mephistopheles. If it is given that Dr. Faust has been everywhere at least once, prove that at some point someone paid no less than $25.
  5. Let’s say there is a gathering where among any three people there are two friends. Is it true that people at such gathering can always be divided into two groups in a way that every two people in one group are friends?
  6. Let me see if i can ask my question better. Suppose you have twelve rods of two different sizes. One size is 4 in. The other is 8 in. There are 8 - 4in. Rods and 4 - 8 in rods. Use the 4 in rods to construct two squares. Stand your squares up perpendicular to your table and parallel to each other. Now take one 8 in rod and connect it to the top left of one square (first square) and bottom left of the other. Take your second rod, connect it to the top right of the first square and top left of the other. Third rod, bottom right of first and top right of second. Connect the last rod to the remaining vertices. All rods will remain straight through this process. Find the volume and compare it to the volume of 4x4x8
  7. The square faces are the front and back. If you think of the congruent squares each having vertices abcd in the same clockwise rotation each resting parallel to the other. Then connect 8 inch edges in the following manner, front A to back B, front B to back C, front C to back D, and front D to back A. How does this volume compare to a standard rectangular prism of 4x4x8?
  8. And?
  9. Suppose you have a rectangular prism with dimensions 4x4x8. Lay this shape down with the small square facing you. We are going to distort this rectangular prism. Take the top left corner of the front square and connect it to the bottom left corner of the back corner, take the bottom left corner of the front and connect it to the bottom right corner of the back, and so on. Keep the short edges 4 and the long edges 8, how do the volumes compare?
  10. I'm am curious if maybe I am missing something with my own problem but every time I fold into the center the vertices sum to relatively similar (maybe human error) value. Perhaps this is helpful.
  11. Good question, for this problem I meant for the move to mean always going to the original center.
  12. You are right!
  13. 4
  14. LOL, thought that was only me. In (dis)proving this, consider what events cause the creation of more than one extra vertex. Then I think you will see.
  15. Wouldn't this depend on the orientation of the rectangle and the circle. I can think of some cases when the centers meet on a line where the line intersects the rectangle at an awkward angle and not cut the circle in half. Or am I missing something?