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

 Messages: [ Previous | Next ]
 Michael Press Posts: 2,137 Registered: 12/26/06
Re: make 100 by using 1, 7, 7, 7, 7
Posted: Nov 14, 2007 9:08 PM

> 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 is a Perl script that prints out all balanced strings
of parentheses. The balanced strings of 2n parentheses
can be bijected with the binary trees on n vertices.

The script works like this:

P_n is the set of balanced strings of 2n parentheses so
P_{n+1} = (P_{k}) P_{n - k}.

The script is criminally wasteful of time and
space, but it is easy to code, an easy to understand. :)

________________________
#!/usr/bin/perl

\$count = \$ARGV[0];

print join "\n", pren(\$count), "";

sub pren
{
my @list = ();

(my \$n) = @_;
if (\$n == 0) {push(@list, "")}
elsif(\$n == 1) {push(@list, "()")}
elsif(\$n > 1)
{
foreach \$k (0 .. \$n-1)
{
foreach \$p1 (pren(\$k))
{
foreach \$p2 (pren(\$n - 1 - \$k))
{
push @list, sprintf "(%s)%s", \$p1, \$p2;
}
}
}
}
return @list;
}
________________________

\$ ./parens.pl 5 | cat -n
1 ()()()()()
2 ()()()(())
3 ()()(())()
4 ()()(()())
5 ()()((()))
6 ()(())()()
7 ()(())(())
8 ()(()())()
9 ()((()))()
10 ()(()()())
11 ()(()(()))
12 ()((())())
13 ()((()()))
14 ()(((())))
15 (())()()()
16 (())()(())
17 (())(())()
18 (())(()())
19 (())((()))
20 (()())()()
21 (()())(())
22 ((()))()()
23 ((()))(())
24 (()()())()
25 (()(()))()
26 ((())())()
27 ((()()))()
28 (((())))()
29 (()()()())
30 (()()(()))
31 (()(())())
32 (()(()()))
33 (()((())))
34 ((())()())
35 ((())(()))
36 ((()())())
37 (((()))())
38 ((()()()))
39 ((()(())))
40 (((())()))
41 (((()())))
42 ((((()))))

--
Michael Press

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