+447 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)
+2862 lez draw a 3 by 3 chess board yeet
| corner | side | corner |
| side | NONE | side |
| corner | side | corner |
*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.
+2862 By the way, I like your riddles, it helps me warm up my brain and makes me feel mentally healthy lol.
