Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Messages: [ Previous | Next ]
 Thomas Nordhaus Posts: 433 Registered: 12/13/04
Re: make 100 by using 1, 7, 7, 7, 7
Posted: Nov 14, 2007 7:52 AM

Robert Israel schrieb:
>

>> On 2007-11-13 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]]]}

Would the program be any simpler if you encoded RPN, that is
+,-,/,E(nter)? The solution then is:

1E7/7+7E7+*

--
Thomas Nordhaus

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