Mock AIME 1 2010 Problems/Problem 2

Problem 2

Find the last three digits of the number of 7-tuples of positive integers $(a_1, a_2, a_3, a_4, a_5, a_6, a_7)$ such that $a_1 \, | \, a_2 \, | \, a_3 \, | \, a_4 \, | \, a_5 \, | \, a_6 \, | \, a_7 \, | \, 6468$ , that is, $a_1$ divides $a_2$ , $a_2$ divides $a_3$ , $a_3$ divides $a_4$ , $a_4$ divides $a_5$ , $a_5$ divides $a_6$ , $a_6$ divides $a_7$ , and $a_7$ divides $6468$ .

Solution

$\boxed{944}$ .

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Mock AIME 1 2010 Problems/Problem 2

Problem 2

Solution

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