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a calculator that can display ten digits. How many different ten-digit numbers can be type using just 0-9 keys once each, and moving from one keypress to the next using the knight’s move in chess? (In chess, the knight move in an L-shape – one square up and two across, two squares down and one across, two squares up and one across, and other like combinations)

 

No web answers

off-topic
 Sep 9, 2019
edited by killersteve27  Sep 9, 2019
 #1
avatar+48 
+5

It has to start on 5 and then go to 0, or else not all of the numbers will go in the knight move pattern. 

We have 5034927618 and 5038167294, plus their opposites (the same number backwards). So only 4 numbers can be formed. 

 

Please correct me if I am wrong! 

 Sep 9, 2019
 #2
avatar+23133 
+6

A calculator that can display ten digits.
How many different ten-digit numbers can be type using just 0-9 keys once each,
and moving from one keypress to the next using the knight’s move in chess?
(In chess, the knight move in an L-shape – one square up and two across, two squares down and one across,
two squares up and one across, and other like combinations)

 

\(\begin{array}{|c|c|} \hline \text{moving from keypress} & \text{to the next} \\ \hline 0 & 3 \text{ or } 5 \\ 1 & 6 \text{ or } 8 \\ 2 & 7 \text{ or } 9 \\ 3 & 4 \text{ or } 8 \\ 4 & 3 \text{ or } 9 \\ 5 & 0 \\ 6 & 1 \text{ or } 7 \\ 7 & 2 \text{ or } 6 \\ 8 & 1 \text{ or } 3 \\ 9 & 2 \text{ or } 4 \\ \hline \end{array}\)

 

The graph is:

 

A Hamiltonian path is a path in this directed graph that visits each vertex exactly once.

 

Here are four Hamiltonian paths:

 

1.

 

2.

 

3.

 

4.

 

laugh

 Sep 10, 2019

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