The king can stand on any space at the edge of a square 201 spaces wide by traveling to it as directly as possible with his 100 moves; diagonally toward it until he shares an X or Y coordinate, then orthogonally toward it the remainder of the distance. All spaces inside this square can also be reached by using the same method while wasting excess moves. If the king reaches his target space with an excess of turns remaining, he can burn them 3 at a time by moving in a triangle, and 2 at a time by moving back and forth. If the king is next to his target space with exactly 2 turns remaining, he must move onto it indirectly by first moving onto an adjacent space. This means he can reach any space within the square, for a total of 40401 spaces.
My answer to the end of the video. The king can go up 100 spaces, can go down 100 space (+ his lane) So 201 lanes total We can do same with columns so there are also 201 columns. So I multiply these numbers : 201² = 40401. Thats my answer. And for n moves, the king can go to S(n)= (2n+1)² squares when n≠1 And with S(1)= 8
Answer about the king (just guessing, didn't think about it a lot): It will be able to reach all squares inside a giant square that's of side 201 (100 in each direction from the starting position), so 40.401 squares?
The king can stand on any space at the edge of a square 201 spaces wide by traveling to it as directly as possible with his 100 moves; diagonally toward it until he shares an X or Y coordinate, then orthogonally toward it the remainder of the distance.
All spaces inside this square can also be reached by using the same method while wasting excess moves.
If the king reaches his target space with an excess of turns remaining, he can burn them 3 at a time by moving in a triangle, and 2 at a time by moving back and forth.
If the king is next to his target space with exactly 2 turns remaining, he must move onto it indirectly by first moving onto an adjacent space.
This means he can reach any space within the square, for a total of 40401 spaces.
For king, it goes 1, 9, 25 ie odd squares. so its (2n-1)^2
n was defined as the number of moves, so for n=1 you get 8 (or 9 for odd squares)
Then you get (2n+1)^2 instead
Technically it goes 1,8,25...
Very cool video with nice idea. I have been entertained and further educated.
Nice video!
My answer to the end of the video.
The king can go up 100 spaces, can go down 100 space (+ his lane)
So 201 lanes total
We can do same with columns so there are also 201 columns.
So I multiply these numbers : 201² = 40401.
Thats my answer.
And for n moves, the king can go to S(n)= (2n+1)² squares when
n≠1
And with S(1)= 8
Answer about the king (just guessing, didn't think about it a lot):
It will be able to reach all squares inside a giant square that's of side 201 (100 in each direction from the starting position), so 40.401 squares?
Enehhehe.