
MU puzzle - bladecatcher
https://en.wikipedia.org/wiki/MU_puzzle
======
arkadiyt
People who like this might also enjoy the similarly simple (yet unsolved)
Collatz Conjecture:

[https://en.wikipedia.org/wiki/Collatz_conjecture](https://en.wikipedia.org/wiki/Collatz_conjecture)

~~~
Intermernet
On a slight tangent, I recently read a paper on an interesting relationship
between Collatz path length and Mersenne primes.

"Our main finding to report is the fact that a path length of a Mersenne prime
is approximately proportional to its index for large n, namely, D(Mn) ≈
13.45n."

Paper is at
[https://arxiv.org/pdf/1104.2804.pdf](https://arxiv.org/pdf/1104.2804.pdf) .
WARNING: PDF.

~~~
jamescostian
I'm curious, why do people on HN warn about PDFs? The worst things I can
imagine happening with PDFs are (1) you don't have any software that can read
it (probably like .2% of HNers?) and (2) it could potentially have some
malware (but the same could be said of a website)

~~~
pronoiac
The mobile experience for PDFs is awful.

~~~
anoncake
The mobile experience for HTML/JS/CSS is awful too.

------
lixtra
When I read about it in Gödel Escher Bach I wasn’t aware yet that unsolvable
is a valid answer to a problem. I felt cheated(1) and the whole book lost a
lot of its appeal.

In retrospect it may have actually undone some damage done by the school
system where the solution space is usually very restricted.

Edit: (1) From what I remember it’s stated as find the sequence and not does
such a sequence exist.

~~~
chongli
I would continue arguing that "unsolvable" is not a valid solution to this
_puzzle_. If the description asks you to "find the solution" and the solution
does not exist, then it is a riddle, not a puzzle.

~~~
ineedasername
You're simply playing semantics and defining "puzzle" as "something that has a
solution".

But if you're at work and your boss says "I have a puzzle I need you to solve:
Given these constraints, find an answer" You need to be able to say "Here is
my solution" or "No solution is possible, and here is why."

Or take something simpler: a 500 piece "Puzzle" only there's a manufacturing
defect in all copies: one piece is miss shaped. The puzzle can't be completed;
there is no "solution". It's still a puzzle.

So no, you don't get to "unfair!" your way out of the MU Puzzle through narrow
semantic definitions, especially given the, well, _grammatical_ nature of
language, because then you have gone and missed the entire point.

~~~
paradoxparalax
I think his point: "If it asks you for a solution that doesn't exist, It's a
Riddle" is a perfectly valid point and your comment was a bit "overreactive",
in my opinion.

~~~
ineedasername
What makes it a valid point? I see nothing in the definition of either word
that would definitively preclude "puzzle" as an appropriate label. Riddle is
fine too, but no mutually exclusive.

You and the parent comment claim it's not a puzzle, it's a riddle, with the
implication that's somehow unfair or deceptive in how the problem was framed.

That is a semantic hair splitting that dodges the problem & its answer. In
real life problems you don't get to define away responsibility for problems
put in front of you. And if thoroughly stating my case is "overractive", then
I'm guilty, but I find it's generally better to over-support my argument than
state claims without justification.

------
amatic
Is the Gödel Escher Bach worth the reading? I started, but I feel it's fluff.
People say he is good, though. Are there some practical insights?

~~~
edflsafoiewq
I think most of us who really like it read it as kids which colors it too
much. I distinctly remember this proof that you can't solve the MU-puzzle as
the first piece of mathematics I ever saw. In one swoop I discovered
impossibility proofs, invariants, and the use of divisibility which suffused
the whole book with an aura of initiation into great mysteries that it will
never attain for the already-initiated.

~~~
justinator
I read it in art school (swiped from my then-girlfriend's bookshelf), and it
was nice to have a connection between my school of art weirdos and putting
myself through the same school by teaching myself software engineering. I
distinctly remembering writing a Perl script to highlight that the Mu puzzle
is unsolvable.

    
    
        #!/usr/bin/perl -w
        use strict; 
    
    
        my %tried = (); 
    
        main(); 
    
        sub main { 
    
            my @rules = (
                         \&rule_one, 
                         \&rule_two,
                         \&rule_three, 
                         \&rule_four,
                        ); 
    
            my $axiom = 'MI';
        
            my @path; 
            my @tries; 
    
             solve($axiom, \@rules); 
        }
    
    
        sub solve { 
    
            my @app; 
    
    
            my ($axiom, $rules) = @_; 
            my $i = 0; 
    
            foreach(@$rules){ 
                my $tmp =  $_->($axiom);
                push(@app, $tmp) if $tmp;
            }
    
            foreach(@app){ 
    
                next if $tried{$_};
                next unless (length($_) < 1000); 
        
                print $_ . "\n";
        
                $tried{$_} = 1; 
        
                if($_ eq 'MU'){ 
                    print "YES!\n\n\n"; 
                    exit;
                }
                solve($_, $rules); 
            }
    
        }
    
    
    
        sub rule_one { 
            # If any string ends in I, you can append U
    
            my $str = shift; 
    
            if ($str =~ m/I$/){ 
                return $str . 'U';     
            }else{ 
                return undef; 
            }
        }
    
    
    
    
        sub rule_two { 
            # If any string begins with M, 
            # you can duplicate the string after M,    
    
            my $str = shift; 
    
            if($str =~ /^M/){ 
                return 'M' . substr($str, 1) . substr($str, 1); 
            }else{ 
                return undef;
            }
        }
    
    
    
    
        sub rule_three { 
            # If any string contains III, 
            # you can replace the III with U
    
            my $str = shift; 
            if($str =~ /III/){ 
                $str =~ s/III/U/g;
                return $str; 
            }else{ 
                return undef;     
            }
        }
    
    
    
    
        sub rule_four { 
            #If any string contains UU, 
            # you can delete the UU
    
            my $str = shift; 
    
            if($str =~ /UU/){ 
                $str =~ s/UU//g; 
                return $str;
            }else{ 
                return undef; 
            }
        }

------
jeromebaek
This was my first introduction to formal language theory. Beautiful intro.

------
paradoxparalax
I have learn more geometry from trying to solve the unsolvable "squaring the
circle" problem than all the Geom. classes I had in my life. For example: No
one ever has told me in school that for all squares, the length of the
diagonal equals The Square Root Of Two times the side of the square's, so for
a square where the side is 1 meter, the diagonal will be Sq.Rt.o'2 meters
(around 1,4 m), And I came to find that by myself doing the exercise of the
unsolvable. Also, more recently early this year, I found that the
diagonal/diameter of a Pentagon was the Cubic Root of 3, or this was the
hexagon, and the heptagon was the S.q.rt.o'2 multiplied by C.rt.o'3 or
something like this, the thing is that they follow a sequence, Its always
something with the square and cubic roots of 2 and 3 and I guess 5 or 7 will
appear later in the sequence for polygons with more sides, noting that for a
"infinite sides 'polygon' " , which would be a circle, the number that relates
the diagonal with the "'sides'", or in this analogy, the Perimeter , is
Pi...Anyway, good exercises. p.s: I have remembered that back then I thought
maybe Pi was Square Root of Infinity, and now just came to my mind that maybe
would be the Infinite Root of something...But off course just joking thinking,
but nice exercise.

~~~
mrleiter
> For example: No one ever has told me in school that for all squares, the
> length of the diagonal equals The Square Root Of Two times the side of the
> square's, so for a square where the side is 1 meter, the diagonal will be
> Sq.Rt.o'2 meters (around 1,4 m), And I came to find that by myself doing the
> exercise of the unsolvable.

That's actually the Pythagorean theorem. How did you arrive at that by doing
the "unsolvable"?

~~~
avian
The “unsolvable problem” the parent refers to is the problem of geometrically
constructing a square with the same area as a circle. It has been proven to be
impossible.

[https://en.m.wikipedia.org/wiki/Squaring_the_circle](https://en.m.wikipedia.org/wiki/Squaring_the_circle)

