Tantrix in the UK and Ireland

Infinite Tantrix Discovery

Note: If you have not already read about how to combine Tantrix Discovery sets to create ever larger puzzles, this page may make more sense if you have a look here first.

In 2001, Clive Fraser, a teacher at Leeds Grammar School, became the first person in the world to come up with a complete system to solve Discovery Puzzles in free-form (i.e. not restricted like the records with real tiles) all the way up to infinity for all of the colour and tile number combinations for which this is possible.

These solutions use ten-tile bridging links which can be combined any number of times ad infinitum to use up all of the complete sets of 10 tiles. The remaining R tiles (eg. R=4 for the solutions with 4, 14, 24, 34 and 44 tiles, etc) are then used to close up each end of the loop.

Clive has provided examples for all of his solution sets. Here is the solution set for R=4. This shows how you can solve for ((10 x N) + 4) tiles, where N is any number between 0 and infinity. Those who are mathematically-minded will no doubt recognise this as a proof by induction that Clive's method works all the way up to infinity. After the example, you will find details of exactly what you need to do if you want to try to match Clive's achievement.

Clive Fraser's infinite repeating solutions for 10N+4 Discovery tiles

Your challenge

Finding even just one of the other sets of solutions is quite a challenge, but if you want to match Clive's achievement you will need to:

  1. Find sets of repeating solutions like the one above for all ten numbered tiles, i.e. one set for 10 N + 1 tiles (N = 1, 2, ... , infinity), one set for 10 N + 2 tiles (N = 1, 2, ... , infinity), one set for 10 N + 3 tiles (N = 0, 1, 2, ... , infinity) and so on all the way up to 10 N + 9

  2. Find separate sets of solutions for each of the three colours for 10 N tiles (N = 1, 2, ... , infinity)

  3. Find the value of R other than 10 for which you can find a solution with a second colour (i.e. not the colour of the number on the back) for 10 N + R when N is 0 and solutions for all three colours for N > 0, then find an infinite set of solutions for each colour for this value of R too
Clive was also the first person in the UK to find new computer solutions for the "four longest loops" and "four longest lines" puzzles.

Happy puzzling!

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