c) Explain why Oliver cannot convert 1 red brick into 5 red bricks in less than 6 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 fo blue and green bricks that is even. out of bricks of one particular colour. So he invented some 3D printingOliver got frustrated sometimes with his somewhat limited set, of se ablue, and green building bricks. Part way through a project, he often Tamachines that transform a brick of one colour into a combination ofbricks of one or more colours. Each machine can also operate in reverseThe red machine (R) converts 1 red brick (r) into 1 blue brick (b) and 1green brick (g). This process and its reverse are represented byRr→ bgand bgR-1r.Similarly, for the blue machine (B) we haveBB-1b→ rgand rg→b.And for the green machine (G) we haveG→ rband rbg.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 1red and 3 green bricks in three steps, as follows:BbbbG-1→ rgggB→ rgbb º→ rgrgbNote that the order of the bricks in each collection is irrelevant.

From the given information. The r, b and g are red, blue and green bricks respectively. The R, B and…

Answered: c) Explain why Oliver cannot convert 1…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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c) Explain why Oliver cannot convert 1 red brick into 5 red bricks in less than 6 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 fo blue and green bricks that is even.

out of bricks of one particular colour. So he invented some 3D printing
Oliver got frustrated sometimes with his somewhat limited set, of se a
blue, and green building bricks. Part way through a project, he often Ta
machines that transform a brick of one colour into a combination of
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 (g). This process and its reverse are represented by
R
r
→ bg
and bg
R-1
r.
Similarly, for the blue machine (B) we have
B
B-1
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 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
bbb
G-1
→ rggg
B
→ rgbb º→ rgrgb
Note that the order of the bricks in each collection is irrelevant.

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