Build a NAND gate using multiple NAND gates A question that had popped up in my head once - how many NAND gates would it take to build a larger, "meta-NAND" gate?

Your task is to build a black-box circuit that takes two input wires A and B and returns one output wire that satisfies A NAND B, subject to the following restrictions:


You must use at least two NAND gates in this construction (and no gates other than NAND).
You may not have null configurations of gates - that is, systems of gates that are equivalent to a gateless wire. (For example, two NOT gates in series are a null configuration.)
You cannot have any stray wires (discarded values or constants).


Fewest gates wins.
Three gates.  Compute (((A nand A) nand B) nand B).  Unlike the four-gate solution above in which three of the four gates compute A nand B, two of them simultaneously, and substituting one of the simultaneous outputs for the other would yield two consecutive inverters, the three-gate solution uses the three gates to compute different functions: "not A", "A or not B", and "A nand B".  Only the last gate computes the desired function.