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rocdocmac

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Posts posted by rocdocmac


  1. Here is another cryptogram:

    XTWUMG YPNGGBNMC DXTAUFFNTMVBBO

    Solve it, then unscramble the letters in the resulting sentence (it is now an anagram) to reveal the name of a rock group and the title of one of their songs (six words altogether).

    Spoiler

    This image is a clue to the solved cryptogram ...

    Clue 1.jpg

     

     


  2. Vertical (in any direction) = straight down.

    Horizontal as in figure, e.g. a cake. Two vertical cuts give 4 pieces, then the 3rd cut (horizontal ) divides those 4 pieces into two each for a total of 8. Horizontal cuts are therefore excluded.

     

    Cutting cake.jpg


  3. 23 hours ago, rocdocmac said:

    Possible solution ... 

      Reveal hidden contents

    Solution.jpg

     

     

    Spoiler
    Spoiler

    Corrected solution..jpg

    Sorry, there is a slight mistake in my image on the left ... one of my dominoes {1+3 @ e5+e6} is upside down, but correct in the right diagram. Here is the correct image.

     

     

     


  4. 8 hours ago, Thalia said:

    I'm not quite sure what you are saying. A domino consists of 2 squares. So while there are 56 squares, there's only 28 dominoes. So for example, A2 and A3 together are a single domino.

    What I'm trying to say is that, if the layout was made by using 2 complete domino sets, there should be two 0-0's and two 6-6's. In the figure there is only one 0-0 and one 6-6. So I guess that the given layout makes use of one 6-6 and one 0-0 only, but adding duplicate dominoes from a third set, e.g. a third 5-5.


  5. All cuts should be vertical and in any direction ... I only emphasized that no horizontal cut is allowed, e.g. one could possibly divide a cake with three cuts to yield 8 pieces ... 2 vertical cuts and 1 horizontal cut!

    (1) 125251 pieces after 500 cuts (correct)

    (2) 3162 cuts gives 500704 pieces  (also correct)

    (3) Never mind the 3rd answer since I reckon that it must be infinity, although 199999 cuts as a first approximation comes very, very close! However, there will always be a remainder of either 1 or a pretty large number.

    Therefore, 2 remains the minimum and maximum  pieces-to-cuts ratio. I cannot, though, prove this mathematically (yet)!

    I wasn't aware of an entry at "Mathworld"! So, my question should actually have been a straight-forward quickie!

     


  6. Thank you Time-LSF! Good one, but ...

    Apology for raising this, but there is only one "double 0" and one "double 6" combination directly adjacent next to each other in the grid, although the total of 56 (7x8) matches twice the number of 28 domino pieces in a normal set! The  "double 1, 2, 3, 4 and 5" are fine.

     


  7. Suppose you have a pizza being cut vertically with one straight cut, you'll be left with two pieces. The ratio of number of pieces to cuts in such an instance will be 2 (a whole number, i.e.  no remainder).

    If you cut a pizza using two straight vertical cuts, you'll have four pieces left (pieces-to-cut ratio = 2, also a whole number).

    Cutting the pizza thrice, the maximum pieces possible is seven (pieces/cuts = 7/3 = 2.3333..., i.e. there is a remainder of 1).

    See attached image.

    Questions ...

    (1) What is the maximum number of pieces that one would get by cutting the pizza 500 times using only straight vertical lines (no horizontal cuts allowed)?

    (2) How many cuts should one make to get a maximum of at least 5 million pieces?

    (3) The minimum piece-to-cut ratio with no remainder is exactly 2 as indicate above. What would be the next higher number of cuts, such that the number of resulting pieces divided by the number of cuts has no remainder?

     

    Pizza cuts.jpg


  8. My answers

     

    Spoiler

    1. 999

    2. 410

    3. 1,2,3

    4. zero

    5. high

    6. 99/99 or 99/.99

    7. no riddle!

    8. 4 (rounding up to the nearest integer = ceiling; any number from 2.000000... to exactly 2.5000000... will round to 2,  not 3)

    9. 31

    10. 120 (permutation 5P4)

    11.  no riddle!

    12. 66 sec.

    13. 9

    14. 20

    15. 2 pages

    16. 600

    17. Masses are the same. Weights differ ... the gold is heavier since it loses less weight in air because of its smaller volume (Archimedes' principle is also applicable to gasses). The weights will only be the same in vacuum.

    18. zero feet

    19. Johnny shouldn't take the bet (!00 % chance  of bringing all $300 back home)

    20. I  have all 6 women, my  friends get none.

     

     

    10 minutes ago, rocdocmac said:

    5. high

    Spoiler

    Changing my answer to the OFF position.

     

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