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The two "Unsolved Tantrix Puzzles" have become an ultimate goal for puzzle addicts worldwide. Designed in 1993, they are two of the hardest Tantrix puzzles ever invented. The Four Longest Lines puzzle remains unsolved without the help of a computer to this day. Both puzzles use all 56 tiles and can be made in any shape. Naturally, the colours of all touching links have to match up and you are not allowed to build holes. The objectives and records in detail for both puzzles:

  • 4 LONGEST LINES: Make four long lines simultaneously, one of each colour. Your score is the combined total of each of the four lines. Only the longest line of each colour counts. Assumed maximum score: 146.

    Best unaided "human" score: 144 - by Angharad Taylor of Great Britain
    Best computer-aided score: 146 - by Jamie Sneddon and Paul Martinsen, New Zealand

  • 4 LONGEST LOOPS: Make four long loops simultaneously, one of each colour. Your score is the combined total of each of the four loops. Only the longest loop of each colour counts. Assumed maximum score: 136.

    Best unaided "human" score: 136 by Jack Kuipers, UK
    Best computer-aided score: 136 by Milan Kuchtiak, Slovak Republic
History of solutions

  • In 1997 Justin Phillips, a third year student at Victoria University in Welllington, New Zealand studying mathematics and computing found a solution for the four-lines puzzle of 139. His score exceeded the previous best solution by eleven points.

  • Soon after Jean Gobet from Lyon, France found a four-loops puzzle solution of 129. His score exceeded the previous best solution by 26 points.

  • In May 1998 Jamie Sneddon and Paul Martinsen, both Auckland, New Zealand, went hunting for the perfect solution to the four-lines puzzle. To make things more efficient they wrote a computer program. The total length of their four-lines solution is 146, seven points longer than the best solution found by any player without computer help:

    "Once we had decided upon the best shape, a nearly regular hexagon, and what sort of pieces were allowed at the edges and corners, I wrote a program to fit tiles into the big hexagon, searching for an arrangement that did not contain any loops. On my computer (a 133Mhz Pentium) the program took more than 50 hours to find the solution, during which time it added and removed tiles more than 4 billion times!"
  • On the 1st of September 1998 we received an email from Slovakia. Milan Kuchtiak had just found two solutions to the four-loops puzzle which exceeded the previous score of 129. Here is his story:

    "Both solutions were found with the help of a computer (Pentium 150). I wrote a program in java which helped me to find the results. In both cases the computer found solutions very close to the final schape. It took me about five minutes to modify these solutions manually to get the final record shape. It took the computer two hours to find the 130-solution and about four hours to find the 136-solution.

    The solution-136 is the best possible solution for this shape (triangle with one attached tile). It seems to also be 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 the 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.

    I was inspired by your web pages - "4 Longest Lines" were also found by the computer. I decided to improve "Loops" because I think that "4 Longest Lines" were already absolute.
  • Once the maximum scores were published, the real challenge left was to solve the Unsolved Puzzles without any computer help. Submissions slowed down. Then in March 2003 Jack Kuipers of London provided an unaided solution for the "Longest Loop" puzzle of 136 , equalling the assumed maximum score. A fantastic achievement, considering that people have been trying to solve this puzzles for many years. Jack comments:
    "I had a few attempts solving it by building up the triangle as I had done for a previous record, then decided on a different tactic. I split the large triangle into four smaller ones, one for each of the colour groups. In the solution you can see that each of the corners and the centre are effectively made up of only one colour group. The corners effectively follow the same pattern as well.

    This reduced the problem to 4 (or rather 2 as the corners were the same) smaller, more tractable ones, and after spending a bit of time reworking the boundary regions, I managed to get a triangular solution while the last piece could be fitted into one of the corners. The whole process took about 12 hours of puzzling since my last record. The above method simplified the problem somewhat, and might make it easier for others to get one of the "perfect" solutions.
  • On the 4th of January 2004 Rob Morton of Knaresborough, Yorkshire broke the world record for the unaided "Four Longest Lines" puzzle with a solution that scores 142.

  • The 26 of August 2005 saw the world record broken once again. Deákné Terkovics Éva of Hungary submitted a solution that scores 143, just 3 less than what we believe to be the theoretical maximum.

  • After more than a year at 143 the record for the unaided "Four Longest Lines" was broken on 20 September, 2006 by Angy Taylor of Great Britain.

    Angy started trying to solve the puzzles in December 2005 but concentrated on the four longest lines because it was still unsolved. She says that she achieved at least forty 141s before one day coming up with a 142. When she finally managed the record breaking 144 she realised that it could be done it four slightly different ways.

    "The only theories I use are, the final shape I want to end up with and where I want the lines to leave. I also find it easier to use crossing tiles at the corners - don't know why though."

    After over a couple of decades of puzzling, one challenge still remains: Find the perfect solution to the "4 Lines" puzzle unaided.

    Good luck!

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    Last update: July, 2017