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Assignment: Due Wednesday, August 29.

                                                     
? ? ? ?      -1     1B A Y []          1G U M []           ?  ?  ?  ?
? ? ? ? <--Pi----   5G U S H ----Pi--> 5B I D S   ---Pi--> ?  ?  ?  ?
? ? ? ?             9W O R M           9W H A T            ?  ?  ?  ?
? ? ? ?            13T I D E          13Y O R E            ?  ?  ?  ?

(1)   Write the orbit notation for Pi.
 Pi = ( 1, 5)( 2,11,15, 7, 8,10,14, 6)( 3,13,12)( 4)( 9)(16)


   2
 Pi  = ( 1)( 5)(2,15, 8,14)(11, 7,10, 6)(3,12,13)( 4)( 9)(16) 

             2    1 B A Y []         1 B  I  T  []
(2)   Find Pi  of 5 G U S H  ======> 5 G  O  R  D
                  9 W O R M          9 W  S  U  Y
                 13 T I D E         13 M  H  A  E

 -1
Pi  =  (16)( 9)( 4)(12,13,3)( 6,14,10, 8, 7,15,11, 2)(5,1)

             -1    1 B A Y []         1  G  R  T  []
(3)   Find Pi   of 5 G U S H  =====>  5  B  A  H  O
                   9 W O R M          9  W  I  D  Y
                  13 T I D E         13  M  U  S  E

(4)   Write the orbit notation of a perfect shuffle.


Here is the formula to get the position of the card.
f[n_] := If[ n >  26,2(n-26),2 n-1];

This iterates the formula.
g[n_] := ( r=n;Do[(Print[r]; r = f[r]), {k,1,10}]);

( 1)
( 2, 3, 5, 9,17,33,14,27)
( 4, 7,13,25,49,46,40,28)
( 6,11,21,41,30, 8,15,29)
(10,19,37,22,43,34,16,31)
(12,23,45,38,24,47,42,32)
(18,35)
(20,39,26,51,50,48,44,36)
(52)



  

(5)  Write the symmetry group of a square.

    1     2
    4     3


(1)(2)(3)(4)       ( 1, 2, 3, 4)   ( 4, 3, 2, 1) 

( 1, 4)( 2, 3)     ( 1, 2)( 3, 4)  ( 1, 3)( 2, 4) 

( 1)( 2, 4)( 3)    ( 1, 3)( 2)( 4)