Onitiu Problem 30x30 Solution

 This was the most difficult to solve so far. It shows a knight tour with 90 degree rotational symmetry with the square numbers in a closed knight path (the red line). There are sixteen cells (marked by squares) where the four circuits intersect. The initial and final cells of each circuit are marked by a darker square (001 and 900 in the case of the circuit of square numbers). 

Solution to Onitiu Problem 30x30

The thick black lines mark single-move links between the circuits. The dotted cells mark the links of two or three moves. These short links place considerable restrictions on the way the paths can be arranged.

Numerologists may notice that the numbers 666 and 216 (6 cubed) occupy diametrically opposite cells. This is because their difference is 450, half of 900.