A probability problem by soumyaranjan ram

Probability Level 4

On a large 999×999 999 \times 999 board, each cell is colored either white or black.

Define a coordinated triple of cells (C1,C2,C3) (C_1, C_2, C_3 ) as the formation such that

  • C1C_1 and C2C_2 are in the same row;
  • C2C_2 and C3C_3 are in the same column;
  • C1C_1 and C3C_3 are white;
  • C2 C_2 is black.

What is the maximum number of coordinated triples? Enter your answer as the last three digits of that maximum.

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