HOME

TREATISE:
. Quantum
Nodal Theory

ROMALDKIRK:
. Village
. Reservoirs

ESSAYS: COSMOLOGY
. Infinity
. Universe
. Dark Matter

ESSAYS: PHILOSOPHY
. Free Will
. Representation
. Conditionals
. Postscript

ESSAYS: ORGAN MUSIC
. Practising
. British Organs
. Hymn Playing
. Music Lovers

QUIZ QUESTIONS
. Monthly Quiz
. Quiz Archive

SERVICES
. Book Reviews

Quiz of the Month (October 2006)

Hector C. Parr

***

SOLUTION TO LAST MONTH'S QUIZ

1.  1/64
2.  7/256
3.  3/64
Notes.
  Notation: H = Head,  T = Tail,  . = either
  Total number of equi-probable permutations of H and T = 210 = 1024

  1.  Number of perms. of form HHHHHH....  = 16
          So probability = 16/1024 = 1/64

  2.  HHHHHHT...      Number of perms. = 8
      THHHHHHT..      Number of perms. = 4
      .THHHHHHT.      Number of perms. = 4
      ..THHHHHHT      Number of perms. = 4
      ...THHHHHH      Number of perms. = 8
                                      -------
                      Total            = 28
          So probability = 28/1024 = 7/256

3. Using a similar method, find the number of permutations with exactly
     six, seven, eight, nine and ten consecutive heads, and add.




  

          
        
        
THIS MONTH'S QUIZ





A coin (resembling a British 20p piece) is in the shape of a "curve of constant width". Each of its seven sides is an arc of a circle whose centre is the opposite vertex. The "radius" of the coin (the distance from the centre to any vertex) is 1 cm.


1. If the coin lies between two parallel lines, as shown, find the distance between the lines.


2. How much less is the circumference of the coin than the circumference of a circular coin with radius 1 cm?


3. How much less is the area of one face of the coin than that of a circular coin with radius 1 cm?




    
***
 


©  Hector C. Parr  (2006)



Go to Quiz Archive



Back to Home Page