24 May
2014
24 May
'14
2:55 p.m.
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