**Martin R. Bridson and Henry Wilton**

A permutoid is a set of partial permutations that contains the identity

and is such that partial compositions, when defined, have at most one extension

in the set. In 2004 Peter Cameron conjectured that there can exist no algorithm

that determines whether or not a finite permutoid based on a finite set can be completed

to a finite permutation group, and he related this problem to the study of groups that

have no non-trivial finite quotients. This note explains how our recent work on the

profinite triviality problem for finitely presented groups can be used to prove Cameron's

conjecture. We also prove that the existence problem for finite developments of rigid

pseudogroups is unsolvable.