The fuel spheres in the core of a pebble-bed reactor are mainly distributed statistically. Regular configurations appear only near the walls and on the bottom of the core. A statistical distribution has been studied by means of a proper mock up. For this purpose the coordinates of 3024 sphere centers were defined by measurements so that Monte Carlo games for neutron diffusion could be established. From these results as well as from Monte Carlo calculations for the cubic and tetrahedral sphere configurations, the diffusion constants and the first two mean moments 
and 
of the passage lengths in the holes were determined. Under the assumption that no correlation exists between the passage lengths in the holes and in the balls, an exact formula for the diffusion lengths was derived using 
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