math
posted by Anonymous .
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 xaxis or the yaxis. 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 Slattice path is a lattice path where every step has size which is a member of S.
Respond to this Question
Similar Questions

Physics
Four particles in the xy plane have the following masses and coordinates: 1 kg at (4 m, 4 m), 2 kg at (−3 m, 5 m), 3 kg at (5 m, −2 m) and 4 kg at (−2 m, −4 m). Find the total moment of inertia about: a) the … 
Algebra
Please help I can't figure out these two. Express f(x) in the form a(x − h)2 + k. f(x) = −4x2 + 24x − 9 Find the standard equation of a parabola that has a vertical axis and satisfies the given conditions. vertex … 
Math
Let S be the set of {(1,1),(1,−1),(−1,1)}lattice path which begin at (1,1), do not use the same vertex twice, and never touch either the xaxis or the yaxis. Determine the largest value of n such that every path in S … 
Geometry
Let S be the set of {(1,1),(1,−1),(−1,1)} lattice path which begin at (1,1) , do not use the same vertex twice, and never touch either the x axis or the y axis. Determine the largest value of n such that every path in … 
math
Let S be the set of {(1,1),(1,−1),(−1,1)}lattice path which begin at (1,1), do not use the same vertex twice, and never touch either the xaxis or the yaxis. Determine the largest value of n such that every path in S … 
math
Let S be the set of {(1,1),(1,−1),(−1,1)}lattice path which begin at (1,1), do not use the same vertex twice, and never touch either the xaxis or the yaxis. Determine the largest value of n such that every path in S … 
help~MATHS
Let S be the set of {(1,0),(0,1),(1,1),(1,−1),(−1,1)}lattice path which begin at (1,1), do not use the same vertex twice, and never touch either the xaxis or the yaxis. Let Px,y be the number of paths in S which end … 
sd224
Let S be the set of {(1,0),(0,1),(1,1),(1,−1),(−1,1)}lattice path which begin at (1,1), do not use the same vertex twice, and never touch either the xaxis or the yaxis. Let Px,y be the number of paths in S which end … 
Math
How many {(1,1),(1,−1),(2,0)}lattice paths are there from the point (0,0) to the line x=8? 
math
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 xaxis or the yaxis. Let Sx,y be the set of paths in S which end …