Re: make 100 by using 1, 7, 7, 7, 7
- From: Michael Press <rubrum@xxxxxxxxxxx>
- Date: Thu, 15 Nov 2007 02:08:03 GMT
In article <2007111313515516807-kirakun@earthlinknet>,
Kira Yamato <kirakun@xxxxxxxxxxxxx> wrote:
On 2007-11-13 13:22:13 -0500, Robert Israel
<israel@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx> said:
"Benjamin A. Bartsch" <benjamin.a.bartsch@xxxxxxxxx> writes:
dangerousgam...@xxxxxxxxx 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
.
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