New ultimate world record!
Congratulations to Jack Kuipers of London, currently at the University of Bristol, who broke the world record for the Tantrix Four Longest Loops puzzle on 10 March 2003 with a solution that scores 136. We believe his score of 136 to be the highest total possible. Jack has sent a picture of it and an explanation of how he got there, but we have not reproduced them here in order to avoid spoiling your fun if you want to try for the ultimate solution yourself.
The previous world record of 133 by Rob Morton of Knaresborough, Yorkshire can be seen above to give you the idea of how the puzzle works. No, you are not seeing things - Rob is colourblind and has painted the green lines on his set white. This little problem has not prevented him from becoming one of the top puzzlers and Tantrix game players in the country!
The Four Longest Loops puzzle, one of the two hardest Tantrix puzzles ever invented, was first fully solved with the aid of a computer by Slovakian Milan Kuchtiak on 1 September 1998. However, the ultimate solution has eluded puzzlers trying to do it without any computer help until now.
Back in 1997, the unaided 'human' record was broken by Jean Gobet of Lyon, France with a score of 129 which exceeded the previous best score by no less than 26 points! Jean's record lasted for five years until the UK players started catching up, with Jack Kuipers himself setting a new world mark of 131 on 28 November 2002. One month later, Rob Morton managed to add two more to Jack's record with the solution that you can see above, and that spurred Jack on to go for the ultimate solution, which he found three months later.
Computer-aided solutions
As mentioned above, Milan Kuchtiak of Slovakia came up with the first ever computer-aided ultimate solution on 1 September 1998. Here is his story of how he found his solution:
"The solution was found with the help of a Pentium 105 computer. I wrote a program in java which helped me to find the results. The computer found a solution very close to the final shape. It took me about five minutes to modify this solution manually to get the final record shape. It took the computer about four hours to find the 136-solution.
The 136-solution is the best possible solution for this shape, i.e. a triangle with one attached tile. It seems to be also the best possible solution for the "4 longest loops", but this needs to be proven.
It took me four days to write and debug the program in java. I was very surprised about the speed of the program, because java belongs to slow programming languages. I decided to write it in java because java is suitable for internet communication - so I was able to send you pictures very quickly.
A few words about me:
I am 37, married, 2 children. I graduated at Comenius University (Mathematics).
Job : project manager (design of computer solutions for construction - buildings, roads)
Hobbies, sport:
I am a paraglider pilot. I participated in slovak paragliding competitions and in some other countries (Austria, Hungary, Czech Republik). I had a small business for 3 years, manufacturing paragliders. I constructed about 7 new paraglider types. Of course these paragliders were designed by computer. I spent some time in a British paragliding school. Besides of flying I like travelling, mountains (before flying I used to climb much), trekking, cycling. I also like to surf the Internet and new inventions in computer technology. I found Tantrix when I was surfing New Zealand's paragliding web pages."
Jaap Scherphuis has made the following comments on whether or not 136 really is the highest possible score for this puzzle:
"It can probably be proved that 136 is the maximum attainable.
Sketch of proof: Any shape with 56 tiles must have some tiles with an odd number of external sides, because they cannot be arranged in a triangle (tiles with 4 external edges are at a 60 degree corner, with 2 external edges along a straight side of the arrangement). Each tile with an odd number of external sides must have at least one line connecting to an internal with an external side. Thus any such odd corner will be the start of a line leading into the arrangement, wasting internal sides which are better used for forming loops. The best shape is therefore one with a small perimeter, but which has few odd corners and has its odd corners close together.
Consider a size 10 triangle with one extra tile added anywhere on its side. This has perimeter 62, and its two odd corners are adjacent so these waste only 2 internal sides. This leaves 336-64=272 internal sides for a total loop length of 272/2=136. Any other shape with more odd corners that is more convex will have a smaller perimeter but all internal sides gained are probably all wasted on the lines between the odd corners. It is likely that no other shapes have more available internal sides.
Again the difficulty is proving that this shape is the best. I have not properly proved this."
If you can come up with an even more conclusive proof than this, please let us know by writing to feedback@tantrix.co.uk.
Go to the main Tantrix UK & Ireland records page
