Simon has learned about a beautiful new game from Alex Bellos on Numberphile. The game is called Loop and resembles pool. The pictures below illustrate the layout on an elliptical game board/pool table. The black hole on the left side is the pool table pocket and the black ball with number 8 on it is the black ball. The white ball is the cuball. The colored balls are the only other balls used in the game. There is a lot of Geometry in this game.
Simon has explained how the pocket and the black ball are located exactly on the focal points of the ellipse, that is why if the black ball is hit (from whatever direction) it is always going to go towards the pocket. The winning strategy in the game would thus be to hit the cuball as if it comes from a focal point.
Simon writing the rules for stages 1 and 2 of the game:
The ball always bouncing at an identical angle:
Thus always hitting the second focal point if coming from the other one:
Never a dull moment sitting down at a summertime terrace together with Simon. Just had a swim at the local pool and thought he was tired, but there he goes: Mom, I’ve got a game for you. Made these 9 cards and taught me how to play: each player grabs one card at a time and whoever has accumulated a valid sum or a set of three operators has won.
It was later that he showed me that the game is actually a number variant of tic tac toe and one should use the same strategy to get three in a row:
Simon talking about his Tantrix Game code and the math behind it. It has been Simon’s first community project, many thanks to everyone who has contributed hexagonal tiles for the game! The game isn’t finished yet, but the video gives a good insight into the work in progress. Simon will finish it at a later date he says. Feel free to try and finish it on your own and share your results! The code is on GitHub at: https://github.com/simon-tiger/tantrix
This is a separate link to see what Simon has got so far in action: https://simon-tiger.github.io/tantrix/tantrix/
Below is Simon’s original YouTube post summoning contributions:
Simon has tried to find out whether each of the players have equally fair chance to win a NIM game. In many games that’s exactly the case, but not in the game of NIM, as Simon proves in the course of these two videos. If you just want to see the math behind it, feel free to only watch the second video:
The game of NIM is about flipping two coins and playing with 12 more coins. Depending on what a player throws (two heads, heads-tails, tails-heads or two heads) she can claim a number of coins from the 12 (corresponding to the binary value of the throw, that can vary from 1 to 4 coins). The person who claims the last coin wins all the 12 of them. Simon has proved that the person starting the game (according to the rules of the game, that’s the person who brought in the money) has better chances of winning!
Simon learned about the game of NIM from Matt Parker’s Stand Up Math channel, but worked out the proof himself.