Question 4: (a) A man places one grain of rice on the first square of a chess board, then two grains on the second square, four on the third square, etc. - every time twice as many as before. Give the exact number of grains on square n, justifying briefly. Calculate how many are on the last square. (2 marks) b) How many squares does one need to fill to get a billion grains of rice? How many, in general, to get M grains of rice? Justify your answers. (2 marks)