Find The Diamond!
There is a diamond hidden on an \(N\times N\) grid at location \((x_D,y_D)\), where \(x_D\) and \(y_D\) are integers.
Every guess, you suggest a pair of coordinates (\(x_G\), \(y_G\)). And, if you get it wrong you are given a hint as to where to go to continue looking. You are told either NW, N, NE, E, SE, S, SW, or W:
- W implies \(x_D < x_G\) and \(y_D = y_G\)
- NW implies \(x_D < x_G\) and \(y_D > y_G\)
If you can get the diamond with 10 guesses or less (i.e. at most 9 wrong guesses and one right one), you get to keep the diamond. What is the largest \(N\) for which you can guarantee success?