1) let there b n signals... now there are four diff signals that can b sent thru each of them. including the pos. of rest.. by ur ques it means that if there is any such combination such that at least one of them does not include the postion of rest then it will constitute a signal... that is only when there are all those n pos of rest it wont constitute a signal..... so each has four options .....so the total diff signals that can b formed is 4*4*4...n times -1 = 4^n-1 .. the 1 is subtracted for the signal when all are pos of rest.. so 4^n-1 = 1023 or n =5