The Cartesian lattice in 2-space. WFL On 5/24/14, Dan Asimov <dasimov@earthlink.net> wrote:
What does "every point" refer to here?
--Dan
On May 24, 2014, at 1:54 PM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
How to destroy any ability at chess which you may previously have enjoyed. Playing from the centre of an infinite open board ---
Q1. Prove that Every point has some knight-move neighbour at smaller knight-move distance from the origin if and only if Every point has some knight-move neighbour at greater knight-move distance from the origin.
Q2. Prove(!) that there is just a single shortest knight path from (0,0) to (2r,r) taking distance r steps.
Q3. Denote e(x, y) the number of shortest knight paths from (0,0) to (x,y) . Prove that e(1999999999, 3) = e(1500000000, 1499999998) .
Fred Lunnon
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