# Find The Diamond!

Logic Level 3

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 $$y_D > y_G$$
• etc.

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?

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