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jasen

Reverse the order of 8 poisonous substances

Question

8 very poisonous substances named s1 to s8 are kept in a safety room.
The substances are kept in ascending order (s1,s2,s3,s4,s5,s6,s7 and s8).
In the room there are 3 robots.

First robot can "rotate left" the order of the substances.
If the order is (a,b,c,d,e,f,g,h) the robot will make it (b,c,d,e,f,g,h,a)

Second robot can split the substances into 2 part then reverse the order of each part.
If the order is (a,b,c,d,e,f,g,h) the robot will make it (d,c,b,a,h,g,f,e)
But the robot is a bit broken, so the resulting order is a bit wrong.
The resulting order will become (d,c,a,b,h,g,f,e).

Third robot can split the substances into 4 part then reverse the order of each part
If the order is (a,b,c,d,e,f,g,h) the robot will make it (b,a,d,c,f,e,h,g)

Questions

If the 2nd robot is not broken, how many minimum step needed by using the robots to reverse the order into descending order? Show the steps!

After the 2nd robot is broken, how many minimum step needed by using the robots to reverse the order into descending order? Show the steps!

Edited by jasen

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4 answers to this question

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Spoiler

For the first type/not-broken robot

5 steps  (a, b, c, d, e, f, g, h)
Robot 1: (b, c, d, e, f, g, h, a)
Robot 1: (c, d, e, f, g, h, a, b)
Robot 1: (d, e, f, g, h, a, b, c)
Robot 1: (e, f, g, h, a, b, c, d)
Robot 2: (h, g, f, e, d, c, b, a)

For the second type/broken robot, need to exploit that asymmetry 6 times, twice reordering in pairs and 6 left shifts, for a total of 14 steps.

14 steps (a, b, c, d, e, f, g, h)
Robot 2: (d, c, a, b, h, g, f, e)
Robot 1: (c, a, b, h, g, f, e, d)
Robot 3: (a, c, h, b, f, g, d, e)
Robot 1: (c, h, b, f, g, d, e, a)
Robot 2: (f, b, c, h, a, e, d, g)
Robot 2: (h, c, f, b, g, d, e, a)
Robot 1: (c, f, b, g, d, e, a, h)
Robot 1: (f, b, g, d, e, a, h, c)
Robot 2: (d, g, f, b, c, h, a, e)
Robot 2: (b, f, d, g, e, a, h, c)
Robot 1: (f, d, g, e, a, h, c, b)
Robot 3: (d, f, e, g, h, a, b, c)
Robot 1: (f, e, g, h, a, b, c, d)
Robot 2: (h, g, f, e, d, c, b, a)

 

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Still working on the second question

Second robot not broken

Spoiler

Robots 2,1,1,1,1

Robot 1 2 3 4 5 6 7 8
2 4 3 2 1 8 7 6 5
1 3 2 1 8 7 6 5 4
1 2 1 8 7 6 5 4 3
1 1 8 7 6 5 4 3 2
1 8 7 6 5 4 3 2 1

 

 

 

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10 hours ago, rocdocmac said:

Does the order of robot function remain constant, i.e. Robot 1, Robot 2, Robot 3, Robot 1, Robot 2, Robot 3, Robot 1, ....?

No, you can choose the robot in each step something like 2213232.....

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