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6 total messages Started by Jim Dars Sun, 10 Oct 1999 00:00
Three Consecutive Numbers
#22
Author: Jim Dars
Date: Sun, 10 Oct 1999 00:00
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Hi All,

Find three consecutive numbers, each divisible by a cube, apart from =
one.

Best wishes, Jim

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<DIV><STRONG><FONT color=3D#0000ff =
size=3D4></FONT></STRONG><STRONG><FONT=20
color=3D#0000ff face=3D"" size=3D4>Hi All,</FONT></STRONG></DIV>
<DIV><STRONG><FONT color=3D#0000ff size=3D4></FONT></STRONG>&nbsp;</DIV>
<DIV><STRONG><FONT color=3D#0000ff size=3D4>Find three consecutive =
numbers, each=20
divisible by a cube, apart from one.</FONT></STRONG></DIV>
<DIV><STRONG><FONT color=3D#0000ff size=3D4></FONT></STRONG>&nbsp;</DIV>
<DIV><STRONG><FONT color=3D#0000ff size=3D4>Best wishes,=20
Jim</FONT></STRONG></DIV></BODY></HTML>

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Letters in the name function
#23
Author: Willse
Date: Sun, 10 Oct 1999 00:00
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All-

Consider the function (whose domain is members of the set Z*, the set of =
nonnegative integers) defined by

LiN(x)=3D{letters in the formal English name of x}

For example, LiN(8)=3D5, because "eight" has five letters.

LiN(x) for the first few values of {0,1,2,...} are =
{4,3,3,5,4,4,3,5,5,4,3...}.

Prove (or disprove) that, regardless of the initial value of x,

{lim n->+oo}[a_n=3DLiN(x) if n=3D1, a_n=3DLiN(a_(n-1)) if n>1]=3D4

Travis J. Willse
sal-crumb@geocities.com


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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META content=3Dtext/html;charset=3Diso-8859-1 =
http-equiv=3DContent-Type>
<META content=3D"MSHTML 5.00.2614.3401" name=3DGENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY bgColor=3D#ffffff>
<DIV>All-</DIV>
<DIV>&nbsp;</DIV>
<DIV>Consider the function (whose domain is members of the set Z*, the =
set of=20
nonnegative integers) defined by</DIV>
<DIV>&nbsp;</DIV>
<DIV>LiN(x)=3D{letters in the formal English name of x}</DIV>
<DIV>&nbsp;</DIV>
<DIV>For example, LiN(8)=3D5, because "eight" has five letters.</DIV>
<DIV>&nbsp;</DIV>
<DIV>LiN(x) for the first few values of {0,1,2,...} are=20
{4,3,3,5,4,4,3,5,5,4,3...}.</DIV>
<DIV>&nbsp;</DIV>
<DIV>Prove (or disprove) that, regardless of the initial value of =
x,</DIV>
<DIV>&nbsp;</DIV>
<DIV>{lim n-&gt;+oo}[a_n=3DLiN(x) if n=3D1, a_n=3DLiN(a_(n-1)) if =
n&gt;1]=3D4</DIV>
<DIV>&nbsp;</DIV>
<DIV>Travis J. Willse</DIV>
<DIV><A =
href=3D"mailto:sal-crumb@geocities.com">sal-crumb@geocities.com</A></DIV>=

<DIV>&nbsp;</DIV></BODY></HTML>

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Re: Three Consecutive Numbers
#24
Author: Tom Crispin
Date: Mon, 11 Oct 1999 00:00
71 lines
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Hi Jim,

Another of Wells' problems if I am not much mistaken.

I am off on a geography field trip for a week with my class of 30 =
nine-year-olds so I'll see you in a week - if this newsgroup has not =
been shut down and I remain sane.

Best wishes, Tom.
    Jim Dars wrote in message ...
    Hi All,
    =20
    Find three consecutive numbers, each divisible by a cube, apart from =
one.
    =20
    Best wishes, Jim

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<HTML>
<HEAD>

<META content=3Dtext/html;charset=3Diso-8859-1 =
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HTML//EN">
<META content=3D'"MSHTML 4.72.3110.7"' name=3DGENERATOR>
</HEAD>
<BODY bgColor=3D#ffffff>
<DIV><FONT face=3DArial size=3D2>Hi Jim,</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
<DIV><FONT face=3DArial size=3D2>Another of Wells' problems if I am not =
much=20
mistaken.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
<DIV><FONT face=3DArial size=3D2>I am off on a geography field trip for =
a week with=20
my class of 30 nine-year-olds so I'll see you in a week - if this =
newsgroup has=20
not been shut down and I remain sane.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
<DIV><FONT face=3DArial size=3D2>Best wishes, Tom.</FONT></DIV>
<BLOCKQUOTE=20
style=3D"BORDER-LEFT: #000000 solid 2px; MARGIN-LEFT: 5px; PADDING-LEFT: =
5px">
    <DIV>Jim Dars<JIM_DARS@EMAIL.MSN.COM> wrote in=20
    message<E2YEP95E$GA.314@CPMSNBBSA03> ...</DIV>
    <DIV><STRONG><FONT color=3D#0000ff =
size=3D4></FONT></STRONG><STRONG><FONT=20
    color=3D#0000ff face=3D"" size=3D4>Hi All,</FONT></STRONG></DIV>
    <DIV><STRONG><FONT color=3D#0000ff =
size=3D4></FONT></STRONG>&nbsp;</DIV>
    <DIV><STRONG><FONT color=3D#0000ff size=3D4>Find three consecutive =
numbers, each=20
    divisible by a cube, apart from one.</FONT></STRONG></DIV>
    <DIV><STRONG><FONT color=3D#0000ff =
size=3D4></FONT></STRONG>&nbsp;</DIV>
    <DIV><STRONG><FONT color=3D#0000ff size=3D4>Best wishes,=20
    Jim</FONT></STRONG></DIV></BLOCKQUOTE></BODY></HTML>

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Re: Letters in the name function
#25
Author: Willse
Date: Mon, 11 Oct 1999 00:00
99 lines
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All-

Oops!  This wasn't supposed to be a reply.  I'll repost it.

Travis J. Willse
sal-crumb@geocities.com


--=20


  Willse <gbtt@email.msn.com> wrote in message =
news:eCe5Fw6E$GA.211@cpmsnbbsa03...
  All-

  Consider the function (whose domain is members of the set Z*, the set =
of nonnegative integers) defined by

  LiN(x)=3D{letters in the formal English name of x}

  For example, LiN(8)=3D5, because "eight" has five letters.

  LiN(x) for the first few values of {0,1,2,...} are =
{4,3,3,5,4,4,3,5,5,4,3...}.

  Prove (or disprove) that, regardless of the initial value of x,

  {lim n->+oo}[a_n=3DLiN(x) if n=3D1, a_n=3DLiN(a_(n-1)) if n>1]=3D4

  Travis J. Willse
  sal-crumb@geocities.com


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<HTML><HEAD>
<META content=3Dtext/html;charset=3Diso-8859-1 =
http-equiv=3DContent-Type>
<META content=3D"MSHTML 5.00.2614.3401" name=3DGENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY bgColor=3D#ffffff>
<DIV>All-</DIV>
<DIV>&nbsp;</DIV>
<DIV>Oops!&nbsp; This wasn't supposed to be a reply.&nbsp; I'll repost =
it.</DIV>
<DIV>&nbsp;</DIV>
<DIV>Travis J. Willse</DIV>
<DIV><A =
href=3D"mailto:sal-crumb@geocities.com">sal-crumb@geocities.com</A></DIV>=

<DIV>&nbsp;</DIV>
<DIV><BR>-- <BR><BR></DIV>
<BLOCKQUOTE=20
style=3D"BORDER-LEFT: #000000 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: =
0px; PADDING-LEFT: 5px; PADDING-RIGHT: 0px">
  <DIV>Willse &lt;<A =
href=3D"mailto:gbtt@email.msn.com">gbtt@email.msn.com</A>&gt;=20
  wrote in message <A=20
  =
href=3D"news:eCe5Fw6E$GA.211@cpmsnbbsa03">news:eCe5Fw6E$GA.211@cpmsnbbsa0=
3</A>...</DIV>
  <DIV>All-</DIV>
  <DIV>&nbsp;</DIV>
  <DIV>Consider the function (whose domain is members of the set Z*, the =
set of=20
  nonnegative integers) defined by</DIV>
  <DIV>&nbsp;</DIV>
  <DIV>LiN(x)=3D{letters in the formal English name of x}</DIV>
  <DIV>&nbsp;</DIV>
  <DIV>For example, LiN(8)=3D5, because "eight" has five letters.</DIV>
  <DIV>&nbsp;</DIV>
  <DIV>LiN(x) for the first few values of {0,1,2,...} are=20
  {4,3,3,5,4,4,3,5,5,4,3...}.</DIV>
  <DIV>&nbsp;</DIV>
  <DIV>Prove (or disprove) that, regardless of the initial value of =
x,</DIV>
  <DIV>&nbsp;</DIV>
  <DIV>{lim n-&gt;+oo}[a_n=3DLiN(x) if n=3D1, a_n=3DLiN(a_(n-1)) if =
n&gt;1]=3D4</DIV>
  <DIV>&nbsp;</DIV>
  <DIV>Travis J. Willse</DIV>
  <DIV><A=20
href=3D"mailto:sal-crumb@geocities.com">sal-crumb@geocities.com</A></DIV>=

  <DIV>&nbsp;</DIV></BLOCKQUOTE></BODY></HTML>

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Re: Three Consecutive Numbers
#27
Author: Jim Dars
Date: Mon, 11 Oct 1999 00:00
101 lines
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Hi Tom,

Good luck with the trip!!  If you were sane when it started (considering =
the situation this might indeed be hypothetical) I expect you'll be sane =
at the finish. =20

Best wishes, Jim
Tom Crispin wrote in message ...
    Hi Jim,
    =20
    Another of Wells' problems if I am not much mistaken.
    =20
    I am off on a geography field trip for a week with my class of 30 =
nine-year-olds so I'll see you in a week - if this newsgroup has not =
been shut down and I remain sane.
    =20
    Best wishes, Tom.
    Jim Dars wrote in message ...
        Hi All,
        =20
        Find three consecutive numbers, each divisible by a cube, apart =
from one.
        =20
        Best wishes, Jim

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<HTML>
<HEAD>

<META content=3Dtext/html;charset=3Diso-8859-1 =
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HTML//EN"><!DOCTYPE HTML PUBLIC "-//W3C//DTD W3 HTML//EN">
<META content=3D'"MSHTML 4.71.1712.3"' name=3DGENERATOR>
</HEAD>
<BODY bgColor=3D#ffffff>
<DIV><STRONG><FONT color=3D#0000ff size=3D4>Hi =
Tom,</FONT></STRONG></DIV>
<DIV><STRONG><FONT color=3D#0000ff size=3D4></FONT></STRONG>&nbsp;</DIV>
<DIV><STRONG><FONT color=3D#0000ff size=3D4>Good luck with the =
trip!!&nbsp; If you=20
were sane when it started (considering the situation this might indeed =
be=20
</STRONG><FONT size=3D4><FONT=20
color=3D#0000ff><STRONG>hypothetical</FONT></FONT><FONT =
color=3D#0000ff><FONT=20
size=3D4>) I expect </FONT></FONT></STRONG><STRONG>you'll be sane at the =

finish.&nbsp; </STRONG></FONT></DIV>
<DIV><STRONG><FONT color=3D#0000ff size=3D4></FONT></STRONG>&nbsp;</DIV>
<DIV><STRONG><FONT color=3D#0000ff size=3D4>Best wishes, =
Jim</FONT></STRONG></DIV>
<BLOCKQUOTE=20
style=3D"BORDER-LEFT: #000000 solid 2px; MARGIN-LEFT: 5px; PADDING-LEFT: =
5px">
    <DIV>Tom Crispin<TOM_CRISPIN@EMAIL.MSN.COM> wrote in=20
    message<OS9RB$6E$GA.310@CPMSNBBSA05> ...</DIV>
    <DIV><FONT face=3DArial size=3D2>Hi Jim,</FONT></DIV>
    <DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
    <DIV><FONT face=3DArial size=3D2>Another of Wells' problems if I am =
not much=20
    mistaken.</FONT></DIV>
    <DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
    <DIV><FONT face=3DArial size=3D2>I am off on a geography field trip =
for a week=20
    with my class of 30 nine-year-olds so I'll see you in a week - if =
this=20
    newsgroup has not been shut down and I remain sane.</FONT></DIV>
    <DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
    <DIV><FONT face=3DArial size=3D2>Best wishes, Tom.</FONT></DIV>
    <BLOCKQUOTE=20
    style=3D"BORDER-LEFT: #000000 solid 2px; MARGIN-LEFT: 5px; =
PADDING-LEFT: 5px">
        <DIV>Jim Dars<JIM_DARS@EMAIL.MSN.COM> wrote in=20
        message<E2YEP95E$GA.314@CPMSNBBSA03> ...</DIV>
        <DIV><STRONG><FONT color=3D#0000ff =
size=3D4></FONT></STRONG><STRONG><FONT=20
        color=3D#0000ff face=3D"" size=3D4>Hi All,</FONT></STRONG></DIV>
        <DIV><STRONG><FONT color=3D#0000ff =
size=3D4></FONT></STRONG>&nbsp;</DIV>
        <DIV><STRONG><FONT color=3D#0000ff size=3D4>Find three =
consecutive numbers,=20
        each divisible by a cube, apart from one.</FONT></STRONG></DIV>
        <DIV><STRONG><FONT color=3D#0000ff =
size=3D4></FONT></STRONG>&nbsp;</DIV>
        <DIV><STRONG><FONT color=3D#0000ff size=3D4>Best wishes,=20
        =
Jim</FONT></STRONG></DIV></BLOCKQUOTE></BLOCKQUOTE></BODY></HTML>

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Re: Three Consecutive Numbers
#30
Author: Tom Crispin
Date: Fri, 15 Oct 1999 00:00
53 lines
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Hi Jim,

Two of the children were HORRENDOUS.  The chap who runs the centre said =
that in his thirteen years dealing with different children every week, =
including EBD (emotional and behavioural difficulty) children, he had =
never come across children with such challenging behaviour.

My sanity was stretched to the limit.  I will spare you the details.

Best wishes, Tom.

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<META content=3Dtext/html;charset=3Diso-8859-1 =
http-equiv=3DContent-Type><!DOCTYPE HTML PUBLIC "-//W3C//DTD W3 =
HTML//EN"><!DOCTYPE HTML PUBLIC "-//W3C//DTD W3 HTML//EN"><!DOCTYPE HTML =
PUBLIC "-//W3C//DTD W3 HTML//EN">
<META content=3D'"MSHTML 4.72.3110.7"' name=3DGENERATOR>
</HEAD>
<BODY bgColor=3D#ffffff>
<DIV><FONT color=3D#000000 face=3DArial size=3D2>Hi Jim,</FONT></DIV>
<DIV><FONT color=3D#000000 face=3DArial size=3D2></FONT>&nbsp;</DIV>
<DIV><FONT face=3DArial size=3D2>Two of the children were =
HORRENDOUS.&nbsp; The chap=20
who runs the centre said that in his thirteen years dealing with =
different=20
children every week, including EBD (emotional and behavioural =
difficulty)=20
children, he had never come across children with such challenging=20
behaviour.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
<DIV><FONT face=3DArial size=3D2>My sanity was stretched to the =
limit.&nbsp; I will=20
spare you the details.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
<DIV><FONT face=3DArial size=3D2>Best wishes, =
Tom.</FONT></DIV></BODY></HTML>

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