Geometric probabilities for hypercubic lattices with hypercubic obstacles in the Euclidean space E_n

In this paper we present a problem of Buffon type for a hypercubic lattice \$\mathfrak\{R'\}^\{(n)\}(L,a)\$ obtained by a hypercubic lattice \$\mathfrak\{R\}^\{(n)\}(L,a)\$ consisting of hypercubic obstacles with edges \$2a\$, having as symmetry center the points \$M_\{h_1,h_2,\ldots,h_n\}=(h_1L,h_2L,\ldots,h_nL)\$, \$h_1,h_2,\ldots, h_n\in \mathbb\{Z\}\$ and the faces parallel to the coordinate planes adding the plane portions delimited by the following segments: \$\\{(x_1,h_2L,\ldots, h_nL):x_1\in [h_1L+a,(h_1+1)L-a]\\}\$, \$\\{(x_1h_1,x_2,h_3L,\ldots, h_nL):x_2\in [h_1L+a (h_1+1)L-a]\\}\$,\ldots,\$\\{(h_1x_1,\ldots,h_\{n-1\}x_\{n 1\},x_n):x_n\in [h_1L+a,(h_1+1)L-a]\\}\$, \$h_1,h_2,\ldots, h_n\in \mathbb\{Z\}\$.