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Mathematical connection problem
There is no solution to this problem. Convert the lattice into a two-dimensional vector matrix.

(0,0)(0, 1)(0,2)(0,3)(0,4)

( 1,0)( 1, 1)( 1,2)( 1,3)( 1,4)

(2,0)(2, 1)(2,2)(2,3)(2,4)

(3,0)(3, 1)(3,2)(3,3) (3 ,4)

(4,0)(4, 1)(4,2) (4,4)

Define the point (n, m) as odd. When n+m is odd and n+m is even, there are 13 even points and 1 1 singularities among the 24 points in the above figure.

Obviously, singularities and singularities cannot be directly connected, even the points are the same, so they cannot be connected as required by the topic.

The topic extends from beginning to end:

Only when the parity points are equal or the difference is 1 can the lattice not be repeatedly connected. However, the points with a difference of 1 shall not be connected end to end.

If possible, designing these points on a cylinder, that is, the problem of space type, will be solved at once.