Posted by **Anonymous** on Wednesday, July 24, 2013 at 5:42pm.

Let S be the set of {(1,1), (1,−1), (−1,1), (1,0), (0,1)}-lattice paths which begin at (1,1), do not use the same vertex twice, and never touch either the x-axis or the y-axis. Let Sx,y be the set of paths in S which end at (x,y).For how many ordered pairs (x,y) subject to 1≤x,y≤31, is |Sx,y| a multiple of 3?

Details and assumptions

A lattice path is a path in the Cartesian plane between points with integer coordinates.

A step in a lattice path is a single move from one point with integer coordinates to another.

The size of the step from (x1,y1) to (x2,y2) is (x2−x1,y2−y1).

The length of a lattice path is the number of steps in the path.

For a set S={(xi,yi)}ki=1, an S-lattice path is a lattice path where every step has size which is a member of S.

## Answer This Question

## Related Questions

- math - Let S be the set of {(1,1), (1,−1), (−1,1), (1,0), (0,1)}-...
- sd224 - Let S be the set of {(1,0),(0,1),(1,1),(1,−1),(−1,1)}-...
- help~MATHS - Let S be the set of {(1,0),(0,1),(1,1),(1,−1),(−1,1)}-...
- math - Let S be the set of {(1,1),(1,−1),(−1,1)}-lattice path which ...
- math - Let S be the set of {(1,1),(1,−1),(−1,1)}-lattice path which ...
- Math - Let S be the set of {(1,1),(1,−1),(−1,1)}-lattice path which ...
- Geometry - Let S be the set of {(1,1),(1,−1),(−1,1)} -lattice path ...
- Math - How many {(1,1),(1,−1),(2,0)}-lattice paths are there from the ...
- Physics - Four particles in the xy plane have the following masses and ...
- Algebra - Please help I can't figure out these two. Express f(x) in the form a(x...

More Related Questions