Not Not

Blogging sure slows down when my life is consumed with marking.

Anyway, heres a new one that was told to me by some people in the math room on KGS:

You have 3 boolean inputs, A, B, and C. You are to set up a circut that has 3 outputs, D, E, and F. You may use as many AND and OR gates as you like, but only 2 NOT gates. Arrange it so that D has the value of NOT A, E has the value of NOT B, and F has the value of NOT C, for arbitrary inputs of A, B, and C.

To put that into a bit more "math" and less "circutry"...give me expressions for NOT A, NOT B, and NOT C, if you can only use NOT twice. You may store variables and use them freely, but you may only call the NOT operator a total of 2 times. For example, you could define P = NOT (A OR B) and then use P as much as you like and that would only count as 1 use of a NOT gate.

For a more general version of the problem, you have 2n+1 inputs to negate, and only n+1 uses of NOT. The general version is fairly tough though, and not very fun.