Oliver spot frustrated sometimes with his somewhat limited set of red We, and green building bricks. Part way through project, he often machines that transform brick of one colour into a combination of cut of bricks of one particular colour. So he invented some 3D printing bricks of one or more colours, Ench machine can also operate in re The red machine (R) converts I red brick (r) into I blue brick (b) 1 groet brick (g). This process and its reverse are represented by R-1 R bg and be Similarly, for the blue machine (B) we have B B- b Tg and Tg +b. And for the green machine (G) we have G-1 g rb and rb The machines can be used on collections of bricks, performing one con version at a time. For example, 3 blue bricks can be converted into 1 red and 3 green bricks in three steps, as follows: B B G- bbb rgbbrgrgb rggg Note that the order of the bricks in each collection is irrelevant. a Show how Oliver can convert 1 red brick into 3 red bricks. b Show how Oliver can convert 1 red brick into 5 red bricks in six steps. c Explain why Oliver cannot convert 1 red brick into 5 red bricks in less than six steps. d Oliver starts with a collection of bricks in which the combined number of blue and green bricks is odd. Explain why he cannot end up with a combined number of blue and green bricks that is even