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Oct 7, 2020
0
#8
Chessguy149 wrote:
In a chess variant, a "lord" can move one space at a time, either upward, or to the right, or diagonally up and to the right. How many ways are there for a lord to move from the bottom left to top right corner of the 8 by 8 chessboard?
Trivial
Oct 7, 2020
0
#9
Chessguy149 wrote:
In a chess variant, a "lord" can move one space at a time, either upward, or to the right, or diagonally up and to the right. How many ways are there for a lord to move from the bottom left to top right corner of the 8 by 8 chessboard?
Edit: my solution does not apply to the right piece.
Let,
a "path" be defined as a sequence of moves that takes a lord from a1 to h8.
a "knight move" be used for the third movement you described the lord being able to make that involves the piece moving diagonally up and then right.
Some few lemmas that are easy to prove:
1. Whatever path the piece takes he ends up moving up(i.e moving from a1 to a2) 7 times and right(i.e moving a1 to b2) 7 times.
2. The knight move is basically moving up once and twice to the right.
3. If C is the number of knight moves in a path, -1>C< 4 for any path
4. We can create a string representation of any path. Imagine a lord going from a1 to a8 and then to h8, we can represent that as UUUUUUURRRRRRR where U means up and R means right. Another example is UUUUUURRRRRK where the K represents a knight move.
My post is getting kinda long so I'll have to shorten it but if you understand everything I've said above, you'll see that we've reduced the problem to working out a few permutation related calculations that add up to the answer of the problem which is 11776.
actually this was part of my math homework (art of problem solving anyone) and i entered 48639 and it was correct. -_-
plus the knight doesn't move twice to the right it moves once
for the problem (not in real chess)
so basically what i mean is that 1. your solution makes no sense and 2. you're wrong
Oct 7, 2020
0
#14
Chessguy149 wrote:
plus the knight doesn't move twice to the right it moves once
I never said the knight moves only twice to the right. What I said was if we had a knight in a1, and it moved diagonally up(a1 to b2) and to the right(b2 to c2) it is the same thing as moving up on step once(a1 to a2) and twice to right(a2 to b2 to c2).
lmao long story short the answer is the 40k one
In a chess variant, a "lord" can move one space at a time, either upward, or to the right, or diagonally up and to the right. How many ways are there for a lord to move from the bottom left to top right corner of the 8 by 8 chessboard?