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Topic: make 100 by using 1, 7, 7, 7, 7
Replies: 41   Last Post: Nov 15, 2007 6:13 PM

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amzoti

Posts: 1,113
Registered: 3/6/07
Re: make 100 by using 1, 7, 7, 7, 7
Posted: Nov 13, 2007 4:10 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Nov 13, 12:05 pm, Robert Israel
<isr...@math.MyUniversitysInitials.ca> wrote:
> Kira Yamato <kira...@earthlink.net> writes:
> > On 2007-11-13 13:22:13 -0500, Robert Israel
> > <isr...@math.MyUniversitysInitials.ca> said:

>
> > > "Benjamin A. Bartsch" <benjamin.a.bart...@gmail.com> writes:
>
> > >> dangerousgam...@gmail.com schrieb:
> > >>> So, using only +, -, x, /, and parentheses, and ONLY these numbers:
>
> > >>> 1, 7, 7, 7, 7
>
> > >>> how can you make 100? Is there more than one solution?
>
> > >> --> (1/7+7)*(7+7)
>
> > >> Benjamin
>
> > > Yes, and that's the only solution (up to commutativity).
>
> > I'm very curious how you concluded this. Was it by a program that
> > tests through all possible combinations?

>
> > I tried to write a program too, but I stop when I couldn't quickly find
> > a way to list out all possible trees with 7 leaves.

>
> Here's my search program, written in Maple.
>
> trees:= proc(S)
> option remember;
> local oper,SL,L,res,ret,V,W,v,w,R,r;
> if nops(S) = 1 then {[op(S),op(S)]}
> else
> res:= {}; ret:= {};
> for oper in [`+`,`-`,`/`,`*`] do
> for SL in combinat[powerset]({$1..nops(S)}) do
> if nops(SL) > 0 and nops(SL) < nops(S) then
> L:= sort([seq(S[j],j=SL)]);
> R:= sort([seq(S[j],j=({$1..nops(S)} minus SL))]);
> V:= trees(L);
> W:= trees(R);
> for v in V do
> for w in W do
> if ((oper = `+`) or (oper = `*`)) and (v[1] > w[1]) then next
> end if;
> try
> r:= oper(v[1],w[1]);
> catch: next;
> end try;
> res:= res union {r};
> ret:= ret union {[r, [v[2],oper,w[2]]]};
> end do
> end do
> end if
> end do
> end do;
> ret
> end if
> end proc;
>

> > select(t -> (t[1]=100), T);
>
> {[100, [[[1, /, 7], +, 7], *, [7, +, 7]]]}
> --
> Robert Israel isr...@math.MyUniversitysInitials.ca
> Department of Mathematics http://www.math.ubc.ca/~israel
> University of British Columbia Vancouver, BC, Canada- Hide quoted text -
>
> - Show quoted text -


Very nice!



Date Subject Author
11/12/07
Read make 100 by using 1, 7, 7, 7, 7
dangerousgame95@gmail.com
11/12/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Thomas Nordhaus
11/12/07
Read Re: make 100 by using 1, 7, 7, 7, 7
amzoti
11/12/07
Read Re: make 100 by using 1, 7, 7, 7, 7
quasi
11/12/07
Read Re: make 100 by using 1, 7, 7, 7, 7
dangerousgame95@gmail.com
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
magidin@math.berkeley.edu
11/12/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Thomas Nordhaus
11/12/07
Read Re: make 100 by using 1, 7, 7, 7, 7
quasi
11/12/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Joshua Cranmer
11/12/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Raymond Manzoni
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
William Elliot
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
amzoti
11/12/07
Read Re: make 100 by using 1, 7, 7, 7, 7
David R Tribble
11/12/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Nat Silver
11/12/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Raymond Manzoni
11/12/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Raymond Manzoni
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Adrian Duma
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
benjamin.a.bartsch@gmail.com
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
amzoti
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
David W. Cantrell
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
magidin@math.berkeley.edu
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
David W. Cantrell
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
magidin@math.berkeley.edu
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
briggs@encompasserve.org
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Robert Israel
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Dave Seaman
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
benjamin.a.bartsch@gmail.com
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
amzoti
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
David W. Cantrell
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Jan Kristian Haugland
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Robert Israel
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Kira Yamato
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Kira Yamato
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Robert Israel
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
amzoti
11/14/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Thomas Nordhaus
11/15/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Michael Press
11/14/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Michael Press
11/15/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Kira Yamato
11/15/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Michael Press
11/15/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Rick Decker
11/13/07
Read Re: make 100 by using 1, 7, 7, 7, 7
Raymond Manzoni

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