!"#$%&"'($)%*'' +,-./0,-1,2'' ,' - - PowerPoint PPT Presentation

0 1 2
SMART_READER_LITE
LIVE PREVIEW

!"#$%&"'($)%*'' +,-./0,-1,2'' ,' - - PowerPoint PPT Presentation

!"#$%&"'($)%*'' +,-./0,-1,2'' ,' 3456778%)$9:;<=>%?*>@99=<="$7)AB7C*:$"79$)%*<3:D9' Rules for Moving Disks !" #$%&'(%)(*+%,)-$%)($%./01%'2%'%3,$4 '''


slide-1
SLIDE 1
  • !"#$%&"'($)%*''
  • +,-./0,-1,2''

3456778%)$9:;<=>%?*>@99=<="$7)AB7C*:$"79$)%*<3:D9'

,'

slide-2
SLIDE 2

Rules for Moving Disks

!" #$%&'(%)(*+%,)-$%)($%./01%'2%'%3,$4'''

''''''E=')%?'D#>='@:'8&#D'@:*')$&&=?:':#F=&':#'=@:3=&'#8' :3='#:3=&':F#':#F=&*G'%**$D@?H'F='#C=;'I$9='J/<'

5" 6(+%02'&1%)7%./010%,802%'*9'+0%:$%/(% '0&$(./(;%)<.$<=%9/2>%0,'**$02%)(%2>$%2)?%'(.% *'<;$02%)(%2>$%:)@),4''

/'

slide-3
SLIDE 3

K%A@?H'%'L#F=&*'#8'M%?#@'N'%:'M#D='

O'

slide-4
SLIDE 4

.'

slide-5
SLIDE 5

P'

slide-6
SLIDE 6

B'

slide-7
SLIDE 7

Q'

slide-8
SLIDE 8
  • '
slide-9
SLIDE 9

Rules for Moving Disks

!" #$%&'(%)(*+%,)-$%)($%./01%'2%'%3,$4'''

''''''E=')%?'D#>='@:'8&#D'@:*')$&&=?:':#F=&':#'=@:3=&'#8' :3='#:3=&':F#':#F=&*G'%**$D@?H'F='#C=;'I$9='J/<'

5" 6(+%02'&1%)7%./010%,802%'*9'+0%:$%/(% '0&$(./(;%)<.$<=%9/2>%0,'**$02%)(%2>$%2)?%'(.% *'<;$02%)(%2>$%:)@),4''

1'

slide-10
SLIDE 10

!" 5!" 5!A!% ,' /' ,' /' .' O' O'

  • '

Q' .' ,B' ,P' P' O/' O,' B' B.' BO' Q' ,/-' ,/Q'

  • '

/PB' /PP'

,R'

slide-11
SLIDE 11

Sequence of Moves for N = 3

  • ,<'SD%99':#'I@H3:<'
  • /<'K="@$D':#'K@""9=<'
  • O<'SD%99':#'K@""9=<'
  • .<'(%&H=':#'I@H3:<'
  • P<'SD%99':#'(=T<'
  • B<'K="@$D':#'I@H3:<'
  • Q<'SD%99':#'I@H3:'

,,'

slide-12
SLIDE 12

First Note from Dr. 4 to Dr. 3

  • “Please do the

“Please do the N = 3 = 3 problem, placing the top 3 problem, placing the top 3 disks currently on Tower #1 disks currently on Tower #1

  • nto Tower #2, the Middle
  • nto Tower #2, the Middle
  • ne. Then pass everything
  • ne. Then pass everything

back to me.” back to me.”

,/'

slide-13
SLIDE 13

Second Note from Dr. 4 to Dr. 3

  • “Now please do the

“Now please do the N = 3 = 3 problem again, this time problem again, this time moving the 3 disks on Tower moving the 3 disks on Tower 2 (Middle) onto Tower 3 2 (Middle) onto Tower 3 (Right). Then pass back to (Right). Then pass back to me.” me.”

,O'

slide-14
SLIDE 14

Note from Dr. 5 to Dr. 4

  • “Please do the

“Please do the N = 4 = 4 problem, placing the top 4 problem, placing the top 4 disks currently on Tower #1 disks currently on Tower #1

  • nto Tower 2, the Middle
  • nto Tower 2, the Middle
  • ne. Then pass everything
  • ne. Then pass everything

back to me.” back to me.”

,.'

slide-15
SLIDE 15

Second Note from Dr. 5 to Dr. 4

  • “Please again do the

“Please again do the N = 4 = 4 problem, placing the 4 disks problem, placing the 4 disks currently on Tower #2 onto currently on Tower #2 onto Tower #3, the Right one. Tower #3, the Right one. Then pass everything back to Then pass everything back to me.” me.”

,P'

slide-16
SLIDE 16

The Good Drs.

,B'

http://image.shutterstock.com/display_pic_with_logo/54820/54820,1283470473,5/stock-photo-students-in-a-classroom-sitting-at-desks-60289693.jpg

3

4

5

6

7

8

9

slide-17
SLIDE 17

The Good Drs.

,Q'

http://image.shutterstock.com/display_pic_with_logo/54820/54820,1283470473,5/stock-photo-students-in-a-classroom-sitting-at-desks-60289693.jpg

3

4

5

6

7

8

9

slide-18
SLIDE 18

The Good Drs.

,-'

http://image.shutterstock.com/display_pic_with_logo/54820/54820,1283470473,5/stock-photo-students-in-a-classroom-sitting-at-desks-60289693.jpg

3

4

5

6

7

8

9

Our focus:

  • Dr. 3, Dr. 4, Dr. 5
slide-19
SLIDE 19

B$&8<0/)(%/0%'%,$2>).%)7%.$C(/(;% 78(&3)(0%/(%9>/&>%2>$%78(&3)(% :$/(;%.$C($.%/0%'??*/$.%9/2>/(%/20% )9(%.$C(/3)(4' '

,1'

slide-20
SLIDE 20

U%):#&@%96'V?'WX%D59='#8'I=)$&*@#? '

  • Y;'"=Z?@[#?G'

–!\]!+!0,2+!0/2^+O2+/2+,2'

  • I=)$&*@#?'F@:3'U%):#&@%96'

–!\]!+!0,2\'

/R'

slide-21
SLIDE 21
  • S#9+.G,GO2'']'S#9+OG,G/2'59$*'S#9+,G,GO2'59$*'S#9+OG/GO2<'
  • _&G'
  • +Y=*:'*=:'#8'D#>=*':#'D#>='.'"@*A*'8&#D'L#F=&',':#'

L#F=&'O2'=`$%9*'

  • +Y=*:'*=:'#8'D#>=*':#'D#>='O'"@*A*'8&#D'L#F=&',':#'

L#F=&'/2'59$*'

  • K#>=D=?:'#8'9%&H=*:'"@*A'8&#D'L#F=&',':#':#F=&'O'

59$*''

  • +Y=*:'*=:'#8'D#>=*':#'D#>='O'"@*A*'8&#D'L#F=&'/':#'

L#F=&'O2''

/,'

slide-22
SLIDE 22

L3='.0a@*A'b&#C9=D '

  • E='3%>='.'"@*A*6'

–SD%99' –K="@$D' –(%&H='' –S$5=&'(%&H='

  • S#9+.G,GO2']'S#9+OG,G/2'b(cS'S#9+,G,GO2'b(cS'

S#9+OG/GO2'

//'

slide-23
SLIDE 23

S#9+OG,G/2']'+S=:'#8'D#>=*':#'D#>='O' "@*A*'8&#D'L#F=&',':#'L#F=&'/2' '

  • ,<'SD%99':#'L#F=&'O<'
  • /<'K="@$D':#'L#F=&'O<'
  • O<'SD%99':#'L#F=&'O<'
  • .<'(%&H=':#'L#F=&'/<'
  • P<'SD%99':#'L#F=&',<'
  • B<'K="@$D':#'L#F=&'/<'
  • Q<'SD%99':#'L#F=&'/<'

DEFG%

/O'

slide-24
SLIDE 24

S#9+,G,GO2']'dK#>=D=?:'#8'eS$5=&' (%&H=f'8&#D'L#F=&',':#'L#F=&'Og' '

DEFG%

/.'

slide-25
SLIDE 25

S#9+OG/GO2']'+S=:'#8'D#>=*':#'D#>=' O'"@*A*'8&#D'L#F=&'/':#'L#F=&'O2' '

  • ,<'SD%99':#'L#F=&'O<'
  • /<'K="@$D':#'L#F=&',<'
  • O<'SD%99':#'L#F=&',<'
  • .<'(%&H=':#'L#F=&'O<'
  • P<'SD%99':#'L#F=&'/<'
  • B<'K="@$D':#'L#F=&'O<'
  • Q<'SD%99':#'L#F=&'O<'

/P'

slide-26
SLIDE 26

L3='h_ciL'_5=&%[#? '

  • h_ciLjS#9+OG,GO2k]i$DC=&'#8'D#>=*'&=`$@&="

' :#'D#>='O'"@*A*'8&#D'L#F=&',':#'L#F=&O<'

  • S#9+OG,GO2]'

–,<'SD%99':#'I@H3:<' –/<'K="@$D':#'K@""9=<' –O<'SD%99':#'K@""9=<' –.<'(%&H=':#'I@H3:<' –P<'SD%99':#'(=T<' –B<'K="@$D':#'I@H3:<' –Q<'SD%99':#'I@H3:'

h_ciLjS#9+OG,GO2k]Q<'

/B'

slide-27
SLIDE 27

H)8(3(;%I)-$0 %

h_ciLjS#9+.G,GO2k]' h_ciLjS#9+OG,G/2kl' h_ciLjS#9+,G,GO2kl' h_ciLjS#9+OG/GO2k<'

/Q'

slide-28
SLIDE 28

h#$?:*6''c*@?H'#$&'M;5#:3=*@* '

  • h_ciLjS#9+!"#G,GO2k']'h_ciLjS#9+!G,G/2kl'

h_ciLjS#9+,G,GO2kl'h_ciLjS#9+!G/GO2kG'#&'

  • h_ciLjS#9+!"#G,GO2k']'

m/!'N',n'l','lm/!'N',n']'' /o/!$l','N'/']''/!"#$$0,<'

/-'

slide-29
SLIDE 29

D<))7%:+%J(.8&3)(' '

/1'

slide-30
SLIDE 30

Final Challenge Problem

  • !']'B.'"@*A*<'
  • K#?A*')#&&=):9;'D#>@?H'#?='"@*A'5=&'

*=)#?"G'=>=&;'*=)#?"<'

  • M#F'9#?H'8#&':3=D':#')#D59=:=':3@*'

K)9$<0%)7%L'()/%5&#C9=Dp'

  • _?='"%;G'#?='F==AG'#?='D#?:3G'#?='

;=%&G':=?';=%&*G',RR';=%&*G'#&'9#?H=&p''

OR'

slide-31
SLIDE 31

WX%D59=*'#8'L&%@9'K%&A=&* '

O,' http://www.dwelement.com/userfiles/image210_lg.jpg http://blog2.bibleplaces.com/uploaded_images/c9a5b936cd51_9237/IsraelTrailmarkeratMachteshRamontb110702007.jpg