Oliver got frustrated sometimes with his somewhat limited set of red, blue, and green building bricks. Part way through a project, he often rah out of bricks of one particular colour. So he invented some 3D printing bricks of one or more colours. Each machine can also operate in reverse. The red machine (R) converts 1 red brick (r) into 1 blue brick (b) and 1 green brick (8). This process and its reverse are represented by r→bg and bg → r. Similarly, for the blue machine (B) we have b → rg and rg → b. And for the green machine (G) we have g→rb and rb→g The machines can be used on collections of bricks, performing one conversion at a time. For example, 3 blue bricks can be converted into 1 red and 3 green bricks in three steps, as follows: bbb → rgbb → rgrgb → 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
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Answer:in 3 times in to the machine of mud
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