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




Re: make 100 by using 1, 7, 7, 7, 7
Posted:
Nov 13, 2007 3:05 PM


Kira Yamato <kirakun@earthlink.net> writes:
> On 20071113 13:22:13 0500, Robert Israel > <israel@math.MyUniversitysInitials.ca> said: > > > "Benjamin A. Bartsch" <benjamin.a.bartsch@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 israel@math.MyUniversitysInitials.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada



