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rocdocmac

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Everything posted by rocdocmac

  1. rocdocmac

    3 Quickies

    10 minutes each! 1. A bag holds four counters. One of them is white. Each of the others is either black or white at equal chance. One randomly draws out two counters, and discover they are both white. If one then randomly draws a third counter, what is the chance that it is white? 2. I’m about to play the music songs on Side 1 of a standard LP (diameter = 292 cm) that contains six tracks. The recorded surface area is 487.6 dm2 (including the “gaps” between each song) and the average distance between each annulus (i.e. distance between each “groove” along the LP radius) is 197 µm. The total time that it will take to play this side right from the beginning of the first song to exactly the end of the last (6th) song is 18:04 minutes. If the “needle” (stylus) is poised 12.5 mm directly above the beginning of the first song and 2 mm away from the edge of the record, how far does the “needle” travel to the point where the last song just ended? 3. What comes next? 6 1 3 1 4 _
  2. rocdocmac

    3 Quickies

    @harey... Êtes-vous Franҫais?
  3. rocdocmac

    3 Quickies

    The needle goes down 12.5 mm to the very beginning of the first song, i.e. before the first song actually starts.
  4. rocdocmac

    Folding and Cutting Paper

    Looks like 21 is a bit stiff. Let's change it to 13.
  5. rocdocmac

    Folding and Cutting Paper

    If a piece of rectangular paper is folded once only and a single straight cut is made in the following ways, how many pieces of paper will there be after the cut paper is unfolded in place? (1) A cut perpendicular to the (last) fold (2) A cut parallel to the (last) fold (3) A diagonal cut (4) A diagonal cut in the opposite direction (5) Both (1) and (2) (6) Both (3) and (4) (7) Both (5) and (6) The answers for cuts (1) to (7) are 2, 3, 3, 3, 6, 7, and 14, respectively. It is very difficult (rather practically impossible) to fold a piece of paper more than 6 or 7 times. But, suppose we have a sheet of paper of infinite size and of negligible thickness, what would the outcome be if such a chunk of paper is folded 21 times and then cut accordingly to the mentioned seven ways? Each new fold from the start of folding is at right angles to the previous one. The images below show the different cuts to be made. The single fold in the given example (or the final fold when multiple folds are involved) appears on the right-hand side (||) of each drawing.
  6. rocdocmac

    Cubicle Stack #2

    @Thalia ... CEEE (76) CEEE Final.xlsx
  7. rocdocmac

    Cubicle Stack #2

    Suppose 27 identical cubes are glued together to form a cubical stack, as illustrated below. If one of the small cubes is omitted, four distinct shapes are possible. If two of the small cubes are omitted rather than just one, twenty-two distinct shapes are possible (see previously submitted Cubicle Stack at BrainDen.com). Now, if three of the cubelets are omitted, how many distinct shapes are possible?
  8. rocdocmac

    Folding and Cutting Paper

    If a piece of rectangular paper is folded once only and a single straight cut is made in the following ways, how many pieces of paper will there be after the cut paper is unfolded in place? (1) A cut perpendicular to the (last) fold (2) A cut parallel to the (last) fold (3) A diagonal cut (4) A diagonal cut in the opposite direction (5) Both (1) and (2) (6) Both (3) and (4) (7) Both (5) and (6) The answers for cuts (1) to (7) are 2, 3, 3, 3, 6, 7, and 14, respectively. It is very difficult (rather practically impossible) to fold a piece of paper more than 6 or 7 times. But, suppose we have a sheet of paper of infinite size and of negligible thickness, what would the outcome be if such a chunk of paper is folded 21 times and then cut accordingly to the mentioned seven ways? Each new fold from the start of folding is at right angles to the previous one. The images below show the different cuts to be made. The single fold in the given example (or the final fold when multiple folds are involved) appears on the right-hand side (||) of each drawing.
  9. rocdocmac

    Sorting out the bar bill

    Does it necessarily mean that all 9 of the teetotalers drank water or is that an assumption? What if some didn't drink at all that day and therefore never touched one of the 106 glasses?
  10. rocdocmac

    Cubicle Stack #2

    @Thalia ... revised MMEE MMEE.xlsx
  11. rocdocmac

    Cubicle Stack #2

    @Thalia ... Please ignore my previous post. Use the later spreadsheet in next message.
  12. rocdocmac

    Cubicle Stack #2

    @ Thalia (4-cubelet removal) ... CEEE.xlsx
  13. rocdocmac

    Cubicle Stack #2

    @Thalia (re 4-cublet removal) ... MMEE.xlsx
  14. rocdocmac

    Right Prime

  15. rocdocmac

    When midnight strikes

    Is Confucious still alive and well?
  16. rocdocmac

    Cubicle Stack #2

    That "19" was a typo, sorry! Latest included ...
  17. rocdocmac

    When midnight strikes

    Kicking of again, if I understand correctly ...
  18. rocdocmac

    Cubicle Stack #2

    ... and above 800 ...
  19. rocdocmac

    Physics fun

  20. rocdocmac

    Cubicle Stack #2

    @Thalia ... Virtually completed counting (4-cubelet removal). Still have to verify, but the total seems to be less than 840!
  21. rocdocmac

    Physics fun

  22. rocdocmac

    Physics fun

  23. rocdocmac

    Physics fun

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