I got the following as an interview question:Count the number of tours from the upper left corner to the lower left corner in a grid world where you can move in any manhattan direction.  This is the number of Hamiltonian paths from upper left to lower left: a path such that every vertex is visited only once, and (this follows from the first statement) such that each edge is used at most once. The grid world is a 4x10 matrix (4 rows and 10 columns). Is it really this hard? Matrix method for counting Hamiltonian cyclesAnd: Number of Hamiltonian Paths from Lower Left to Upper RightThese papers seem dated--94, 97--but are they really asking a question that qualifies for publishing in a combinatorical journal? Then I ran into this: SO question: number of Hamiltonian pathsAnd am thinking dynamic programming, or divide and conquer...but it is really not clear how one would go about doing this. Is there a way to solve this problem in reasonable time? 
Number of hamiltonian tours from upper left to lower left corner of a grid graph?
dynamic programming;discrete mathematics;divide and conquer;hamiltonian path