In the last lecture we saw that t<n/3 is a necessary condition for byzantine agreement. We shall now see that this condition is also sufficient. We will give two solutions. The first is impractical, for it uses exponential time, storage and message size. It is, however, the first solution ever given and its proof is clean [30,23]. The second was developed several years later. It is much more efficient- the cost is only polynomial- and uses interesting techniques [27].