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C# vs. VB contest - Resolving Mac Mahon problem using .NET

, 14 Mar 2005
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Rather than discussing for ever wether C# is better than VB or vice-versa, let's see which programmers are best.

Sample Image - macmahon2.png

Introduction

For the last two years, every couple of month or so an article appears claiming “C# is faster than VB.NET”. I agree C# is possibly very slightly faster, I won’t argue. Perhaps it is only fair. Perhaps it is to compensate the fact that C# programmers are probably not as good a VB programmers. You understand that, it is time to revive a good old war like we had years ago between Atari and Amiga. If we can't decide which Language is best, let's see which programmers are best, whether it is VB programmers or C# programmers.

The Mac Mahon problem

The problem I want to challenge you is this one.

You have to complete a puzzle made of 24 pieces. The pieces are displayed in the picture at the beginning of this article.

  1. All the 24 pieces must be used.
  2. Each piece can be rotated to any orientation.
  3. Each segment color must match the color of the adjoining segment.
  4. The puzzle border must be of the same color (red in this case).

This problem can be reproduced on cardboard to play as a solitaire.

A valid solution

This is one solution of the problem.

As you can see

  • It uses all 24 pieces.
  • The border is all red.
  • Each piece shares a color with each of its neighbours.

The Challenge

The challenge is to make a program which looks for solution for this puzzle. The program has to count how many solutions the puzzle has, and then do it as fast a possible. The existing code is already searching, but not very fast. I let my computer run 24 hours and it did not complete…

VB.NET results

Date Description Result
14/03/2005

First release
by Pascal GANAYE

10,000 results in more than 24 hours. Did not complete
15/03/2005 Added a few optimizations 106624 solutions in 90 minutes

C# results

Date Description Result
14/03/2005

No submission yet

-
17/03/2005 Marc Clifton started a C#. 77,306 solutions in about 60 minutes

Other languages

I would love to see another language here. If you have a try, please post something in the forum below.

Point of Interest

As you can see, each piece is divided in 4 triangles and filled with 3 colours. Mathematically this is a nice problem, because this it is not 24 arbitrary chosen pieces but every single combination. There are 3*3*3*3 = 81 possibilities. But If you remove the duplicates you end up with only 24 different pieces.

Submission rules

  • I will post one submission in each submitted language. You can also use this page forum at the bottom.
  • The program can use any sort of optimisation as long as it stays managed .NET and native language (can’t use MSIL).
  • All optimisation must be described. Please no hard coded solution.

I suggest a notation structure for the solutions. If you name the piece A0,B0,C0,...X0.

Sample screenshot A0 Sample screenshot B0 Sample screenshot C0 Sample screenshot D0 Sample screenshot E0 Sample screenshot F0
Sample screenshot G0 Sample screenshot H0 Sample screenshot I0 Sample screenshot J0 Sample screenshot K0 Sample screenshot L0
Sample screenshot M0 Sample screenshot N0 Sample screenshot O0 Sample screenshot P0 Sample screenshot Q0 Sample screenshot R0
Sample screenshot S0 Sample screenshot T0 Sample screenshot U0 Sample screenshot V0 Sample screenshot W0 Sample screenshot X0

The rotated version of Sample screenshot B0 would be called:

Sample screenshot B1 (90 degrees anti-clockwise)

Sample screenshot B2 (180 degrees), and

Sample screenshot B3 (270 degrees).

Then a solution like this one

could be written like this:

B2 D0 I0 L0 J0 G0
A0 C2 V0 S0 T2 O3
K0 F0 X0 W0 U0 Q3
H2 E0 P2 R2 M2 N3

or even as a single line like this:

B2D0I0L0J0G0A0C2V0S0T2O3K0F0X0W0U0Q3H2E0P2R2M2N3

This will probably help to compare our results.

You can see mine here.

Last notes

I hope you realize, I don't take this language war very seriously. I just love the Mac-Mahon problem. How can we live without knowing for sure how many solutions there are?

License

This article has no explicit license attached to it but may contain usage terms in the article text or the download files themselves. If in doubt please contact the author via the discussion board below.

A list of licenses authors might use can be found here

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About the Author

Pascal Ganaye
Software Developer (Senior)
United Kingdom United Kingdom
I am a French programmer.
These days I spend most of my time with the .NET framework, JavaScript and html.

Comments and Discussions

 
GeneralYour link is incorrect PinmemberMustafa Ismail Mustafa22-Nov-07 12:13 
GeneralRe: Your link is incorrect PinmemberPascal Ganaye7-Jan-08 0:35 
General5784 PinmemberColinDavies17-Apr-05 0:21 
GeneralRe: 5784 Pinmemberpascal ganaye20-Apr-05 14:53 
GeneralI am a bit embarassed... Pinmemberpascal ganaye9-Apr-05 13:12 
GeneralIf this is what I think it is... PinmemberDaniel Turini7-Apr-05 0:53 
GeneralResults Pinmemberpascal ganaye6-Apr-05 10:08 
GeneralRe: Results PinmemberGiancarlo Aguilera7-Apr-05 14:06 
GeneralC++ solution PinmemberJon5-Apr-05 0:34 
GeneralRe: C++ solution PinmemberSeveredCross5-Apr-05 16:44 
GeneralRe: C++ solution PinmemberJon5-Apr-05 22:36 
GeneralRe: C++ solution Pinmemberpascal ganaye6-Apr-05 10:12 
GeneralRe: C++ solution PinprotectorMarc Clifton9-Apr-05 7:16 
GeneralSolved in 67 seconds PinprotectorMarc Clifton31-Mar-05 3:53 
GeneralRe: Solved in 67 seconds Pinmemberpascal ganaye31-Mar-05 9:40 
GeneralRe: Solved in 67 seconds PinprotectorMarc Clifton31-Mar-05 10:56 
GeneralRe: Solved in 67 seconds Pinmemberpascal ganaye1-Apr-05 9:09 
GeneralC# Algorithm PinmemberSeveredCross21-Mar-05 11:05 
GeneralRe: C# Algorithm Pinmemberpascal ganaye21-Mar-05 12:53 
GeneralOptimizations Pinmemberpascal ganaye19-Mar-05 3:48 
Generalhttp://www.ganaye.com/macmahon/ Pinmemberpascal ganaye16-Mar-05 13:08 
General5.2 million and counting PinprotectorMarc Clifton16-Mar-05 0:36 
GeneralRe: 5.2 million and counting Pinmemberpascal ganaye16-Mar-05 11:21 
GeneralRe: 5.2 million and counting PinprotectorMarc Clifton16-Mar-05 15:01 
GeneralThe number of results battle. Pinmemberpascal ganaye16-Mar-05 11:52 

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