Wednesday, 31 March 2021

The Onitiu Problem

 In 1939 in Fairy Chess Review the Romanian problemist Valeriu Onitiu solved the difficult problem of constructing a symmetric chessboard knight tour with the squares in a knight circuit. It turned out that there is only one possible solution. 

I have been looking at this problem to see if it is solvable on larger boards. Initially I found it very difficult. However eventually on 27 March I found a solution on the 16x16 board (which can be split up into 4x4 sections which makes the solution by 'squares and diamonds method' feasible). This quickly led to solution on the 14x14 board, then on the 12x12 board, and finally tonight I solved the 10x10 case. I posted a copy on Twitter (misdated 2921). Here is a better presentation using coloured lines to mark the sequence of squares and the sequence of their complements.

I think I will reserve the other solutions for publication elsewhere in some chess or mathematics journal, where I can write it up in more detail. 

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