The Hurried King
A king stands at the lattice point (0, 0) and wants to reach (5, 5). Each move takes it one unit east (to (x + 1, y)), one unit north (to (x, y + 1)), or one unit diagonally northeast (to (x + 1, y + 1)). How many different sequences of moves take it from (0, 0) to (5, 5)? Give an integer.
Related problems & prerequisites
Worth solving first
- Ten People, Five Pairs 3.0/10
- Arranging MISSISSIPPI 3.0/10
- Paths Below the Diagonal 3.0/10
Source: Classic exercise in wide circulation; no traceable original source. Statement written for AxiomIQ.