I recently discovered the "KenKen" puzzle and have been trying to figure out some of the mathematics behind it. This led me to the following question:
Given an N x N grid, what is the minimum number of filled-in spaces ("clues") needed to define a unique grid, where we must satisfy the requirement that every row AND every column contains exactly one of the integers 1 through N.
It's easy to gather that it depends not only on the number of clues, but on their values as well. For example, the following clues define a unique 3x3 grid
but a 3x3 grid with only 1's on the diagonal does NOT define a unique grid.
Does anyone have any insights into this (or other KenKen-related) problems? it is a very interesting topic indeed.