The simultaneous equations on the Boolean variables $$x, y, z$$ and $$w,$$ $$$x+y+z=1$$$ $$$xy=0$$$ $$$xz+w=1$$$ $$$xy + \overline z \overline w = 0$$$
have the following for $$x, y, z$$ and $$w,$$ respectively.

The number $$43$$ in $$2's$$ complement representation is

An $$n\,\, \times \,\,n$$ array v is defined as follows v[i, j] = i - j for all i, j, $$1\,\, \le \,\,i\,\, \le \,\,n,\,1\,\, \le \,\,j\,\, \le \,\,n$$ The sum of elements of the array v is

The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 cards to guarantee that three cards are from same suit is