  A task is a distributed problem for $n$ processes, in which each process
starts with a private input value, communicates with other processes, and
eventually decides an output value. A task is colorless if each process can
adopt the input or output value of another process. Colorless tasks are well
studied in the non-anonymous shared-memory model where each process has a
distinct identifier that can be used to access a single-writer/multi-reader
shared register. In the anonymous case, where processes have no identifiers and
communicate through multi-writer/multi-reader registers, there is a recent
topological characterization of the colorless tasks that are solvable when any
number of asynchronous processes may crash.
  In this paper we study the case where at most $t$ processes may crash, where
$1 \le t < n$. We prove that a colorless task is $t$-resilient solvable
non-anonymously if and only if it is $t$-resilient solvable anonymously. This
implies a complete characterization of colorless anonymous t-resilient
asynchronous task computability.
