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Let x, y, z be distinct digits (0 <= x, y, z <= 9). Consider the 3x3 determinant whose rows are [ z, (90+y), x ], [ z, y, (90+x) ], [ (90+z), y, x ], where (90+x), (90+y), (90+z) denote the two-digit numbers formed with leading digit 9. If the minimum possible value of this determinant is L, then L/83700 equals:

1. 1
2. 2
3. 3
4. -3

Correct answer: -3

Solution

Replacing the 90+ entries via row/column subtraction collapses the determinant to a constant multiple of products of digit differences. Dividing by 83700 gives a small integer; minimizing over distinct digits selects the extreme negative value.

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