The Infinite Game of Chess (with Outray Chess)
Channel: singingbanana
Category: Education
Tags: sequencegamechessproblemmathematicsmathspuzzlethue-morsemathoutray chess
Description: An infinite game of chess with the Thue-Morse sequence. To avoid an infinite game of chess there was a rule that declared that a game would end if any sequence of moves were repeated three times in a row. However Dutch mathematician Max Euwe showed that the Thue-Morse sequence can define an infinite game since it contains no finite sequence that is repeated three times in a row. The Thue-Morse sequence is made from building blocks of 0110 and 1001, so we know it cannot contain short repetitions like 000, 111, 010101 or 101010. Double digits in the Thue-Morse sequence always appear in the odd positions (starting from position zero), which is not possible if a sequence of odd length is repeated. So the Thue-Morse sequence does not contain any finite sequence of odd length repeated three times in a row. If we remove every second digit of the Thue-Morse sequence we will still have the Thue-Morse sequence. If you apply this to any finite sequence of even length that is repeated three times in a row, you will get a sequence half the length that also repeats three times in a row. Repeat this process until you reach a sequence of odd length repeated three times or a short sequence repeated three times. Since we know this shorter repeated sequence is not contained in the Thue-Morse sequence it implies the original repeated sequence is not contained in the Thue-Morse sequence. The argument above is enough to show that the Thue-Morse sequence does not contain a finite sequence of any length repeated three times in a row. You can read a little more detail here homepages-fb.thm.de/boergens/english/problems/problem059englloe.htm Thanks to Outray Chess for making this video. Outray Chess youtube.com/channel/UCVfSsCg38hOzrezIFvMz9oA/featured Host: Rune Friborg Camera: Mathis Eskjær Editing: Mathis Eskjær and Rune Friborg Finally, here is our video about Hugh Alexander, as promised youtu.be/im75EwDXEzg
