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I have a calculator that can display ten digits. How many different ten-digit numbers can I type using just the 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)

off-topic
 Nov 1, 2019
 #1
avatar+2417 
+1

lez draw a 3 by 3 chess board yeet

 

cornersidecorner
sideNONEside
cornersidecorner

*amazing chess board*

 

A knight moves like this (I play chess so its pretty easy for me to visualize)

 

Since a knight moves one square up and two across, two squares down and one across, two squares up and one across, and other like combinations. (or an L shape)

 

it cannot move if it was placed in the center square

 

So there is only eight other squares it can move around.

There are two types, a corner square and a side square

 

Lets count number of ways you can type 10 digit numbers for a CORNER square.

 

Lets list number of combinations of ten digit numbers

 

Digit 1 - 2 ways, because the knight can only move on these directions

 

Digit 2 - 2 ways

 

Digit 3 - 1 way, there is only one way to go back.

 

Digit 4 - 2 ways, starting a pattern

 

Digit 5 - 1 ways

 

Digit 6 - 2 ways

 

Digit 7 - 1 ways

 

Digit 8 - 2 ways

 

Digit 9 - 1 ways

 

Lets calculate. 2 * 2 * 1 * 2 * 1 * 2 * 1 * 2 * 1 = 32

 

32 * 4 (corner squares) = 128 corner ways.

 

Now lets start the sides

 

Digit 1 - 2 ways


Digit 2 - 1 ways

 

Digit 3 - 2 ways

 

Digit 4 - 1 ways

 

Digit 5 - 2 ways

 

Digit 6 - 1 ways

 

Digit 7 - 2 ways 

 

Digit 8  - 1 ways

 

Digit 9 - 2 ways

 

so 2 * 2 * 2 * 2 * 2 = 32 ways

 

32 * 4 = 128 ways

 

128 + 128 = \(\boxed{256}\) ways

 

 

 

PHEW ! Someone check this, I probably over counted.

 Nov 2, 2019
edited by CalculatorUser  Nov 2, 2019
 #2
avatar+2417 
0

By the way, I like your riddles, it helps me warm up my brain and makes me feel mentally healthy lol.

 Nov 2, 2019

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