We show some results related to the classical Banach-Tarski paradox in the setting of finite-dimensional normed spaces over a non-Archimedean valued field K. For instance, all balls and spheres in Kn, and the whole space Kn (for n≥2
Nearby in the stack
) are paradoxical with respect to certain groups of isometries of
Kn
. If
K
is locally compact (e.g.,
K
is the field
Qp
of
p
-adic numbers for any prime number
p
), any two bounded subsets of
Kn
with nonempty interiors are equidecomposable (and paradoxical) with respect to a certain group of isometries of