We consider a model of teaching in which the learners are consistent and have bounded state, but are otherwise arbitrary. The teacher is non-interactive and ``massively open'': the teacher broadcasts a sequence of examples of an arbitrary target concept, intended for every possible on-line learning algorithm to learn from. We focus on the problem of designing interesting teachers: sequences of examples that allow all capable and consistent learners to efficiently learn concepts, regardless of the underlying algorithm used by the learner. We use two measures of efficiency: the number of mistakes made by the worst-case learner, and the maximum length of the example sequence needed for the worst-case learner. Our results are summarized as follows:

- Given a uniform random sequence of examples of an n-bit concept function, learners (capable of consistently learning the concept) with s(n) bits of state are guaranteed to make only O(ns(n)) mistakes and exactly learn the concept, with high probability. This theorem has interesting corollaries; for instance, every concept c has a sequence of examples can teach c to all capable consistent on-line learners implementable with s(n)-size circuits, such that every learner makes only O(s(n)2) mistakes. That is, all resource-bounded algorithms capable of consistently learning a concept can be simultaneously taught that concept with few mistakes, on a single example sequence.

We also show how to efficiently generate such a sequence of examples on-line: using Nisan's pseudorandom generator, each example in the sequence can be generated with polynomial-time overhead per example, with an O(ns(n))-bit initial seed.

- To justify our use of randomness, we prove that any non-trivial derandomization of our sequences would imply circuit lower bounds. For instance, if there is a deterministic 2nO(1) time algorithm that generates a sequence of examples, such that all consistent and capable polynomial-size circuit learners learn the all-zeroes concept with less than 2n mistakes, then EXP P poly.

- We present examples illustrating that the key differences in our model -- our focus on mistakes rather than the total number of examples, and our use of a state bound -- must be considered together to obtain our results.

- We show that for every consistent s(n)-state bounded learner , and every n-bit concept that is capable of learning, there is a custom ``tutoring'' sequence of only O(ns(n)) examples that teaches the concept. That is, in principle, there are no slow learners, only bad teachers: if a state-bounded learner is capable of learning a concept at all, then it can always be taught that concept quickly via some short sequence of examples.