Question

In a chess variant, a "lord" can move one space at a time, either upward, or to the right, or diagonally upward 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?


Thanks in advance for helping me!

Answer 1

Each move advances either upward or rightward or both. If there are n diagonal moves, then there are 14-n up or right moves. So, there may be 0 to 7 diagonal moves, and the rest can be chosen in two ways.

so, there are

(0+2^14) + (1+2^12) + (2+2^10) + ... + (7+0) = 21872

Answer 2

ok thanks alot steve you really help alot

Answer 3

steve is wrong...

Answer 4

You are wrong

Answer 5

You guys....actually try to help out please.

Here, make a chart that cascades to the upper-right-most square. Kinda like Pascal's Triangle.

1............. 48639
1...................
1...................
1...................
1 7 25..............
1 5 13 .............
1 3 5 7 9...........
1 1 1 1 1 1 1 1 1 1 1

So the answer is 48639.

Answer 6

S_Dog is right, Steve is wrong!

Answer 7

thank you s_dog for helping

Answer 8

Thanks s_dog

Answer 9

There are literally more poeple saying 'thanks' than actually giving answers
But yes thank you

Answer 10

i don't understand

Answer 11

all u people just put... and say oh this is the answer

Answer 12

and then everyone is like ur so smart and all like what **** is this

Answer 13

and you're sitting here talking to yourself to a question that was answered 6 years ago

Answer 14

and was, in fact, asked 7 years ago,
and today it would be 8

Answer 15

Why do you guys cheat so much?

Answer 16

Exactly lol

Answer 17

ikr smh