A chess king starts at a position A in the top row of a standard chessboard. The number of paths of length 7 to a
position B in the bottom row is a perfect square, but not a perfect cube.
The number of paths of length 7 from A
to a position C in the bottom row is a perfect cube, but not a perfect square.
The number of paths of length 7 to a
position D is both a perfect square and a perfect cube.
How many chess king paths of length
5 are there from B to C?
Not to much easier but it is also possible to do this for the second part:
In an infinite grid there are 160 possible 5lenght paths from a square to another in the same row at distance four.
¿How you do know this? Because of the polinomial formula

Posted by armando
on 20160603 05:40:31 