Robot factory permutation riddle

In summary, a factory has created a robot that moves on all squares of a 6*6 table, reading and changing the arrows on each square it passes over. After moving twice over each square, it is observed that all the arrows are back to their original direction, indicating that the robot has followed a path from the first square to the last and back again.
  • #1
mathnice1
2
0
A factory has built a robot which moves on all squares of a 6*6 table. There is an arrow On all of the squares of the table when it moves on an square it reads the arrow the square and moves according to the square but before doing that it changes the arrow of the square aim to the previous square(except the 1st square because there was not any squares before that .)...after some moving we understand that the robot has moved on all of the squares for 2 orders (except the first square) show that all of the arrows are the same as the first
sorry for my bad English
 
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  • #2
I assume that "moves according to the square" means that it moves to the square the arrow is pointing to. Does "has moved on all of the squares for 2 orders" mean it has moved twice over each square?
 
  • #3
HallsofIvy said:
I assume that "moves according to the square" means that it moves to the square the arrow is pointing to. Does "has moved on all of the squares for 2 orders" mean it has moved twice over each square?
exactly
 
  • #4
Surely if the robot has passed over each square exactly twice, the robot has followed some path from the first square to the last, and the last square he stands on changes to point back to the square he came from.
This means he will follow that same path to get back to the start and will have stepped on each square twice, thereby reverting all the arrows to their original direction.

EDIT:I denoted the robot as a 'he', I apologize if the robot is actually a female :)
 

1. What is the "Robot factory permutation riddle"?

The Robot factory permutation riddle is a puzzle in which there are four different types of robots (A, B, C, and D) and four different stations (1, 2, 3, and 4). The goal is to figure out how many unique ways the robots can be placed at the stations without any of the same type of robot being adjacent to each other.

2. How many solutions are there to the riddle?

There are exactly 24 unique solutions to the Robot factory permutation riddle. This is because there are 4! (4 factorial) ways to arrange the robots at the stations, but only 24 of these solutions meet the criteria of not having any robots of the same type next to each other.

3. Can the riddle be solved using a formula?

Yes, there is a formula that can be used to solve the Robot factory permutation riddle. It is n! / (n-r)! where n is the number of items to be arranged and r is the number of items that must not be adjacent to each other. In this case, n=4 and r=4, giving us 4! / (4-4)! = 4! / 0! = 4! = 24 unique solutions.

4. Are there any shortcuts or strategies for solving the riddle?

Yes, there are a few strategies that can make solving the Robot factory permutation riddle easier. One is to start with placing the robots that have the most restrictions (in this case, A and D) in the middle stations (2 and 3) first. Another strategy is to think about the number of possible combinations for each station as you go, and try to choose a placement that will give you the most options for the remaining stations.

5. Are there any real-world applications for the riddle?

The Robot factory permutation riddle can serve as a fun and challenging logic puzzle, but it also has practical applications in fields such as mathematics, computer science, and engineering. For example, it can be used to model and solve problems related to scheduling, optimization, and resource allocation.

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