Difference between revisions of "Mock AIME 3 Pre 2005 Problems/Problem 8"

Revision as of 08:32, 14 February 2008

Let $N$ denote the number of $8$ -tuples $(a_1, a_2, \dots, a_8)$ of real numbers such that $a_1 = 10$ and

$\left|a_1^{2} - a_2^{2}\right| = 10$

$\left|a_2^{2} - a_3^{2}\right| = 20$

$\cdots$

$\left|a_7^{2} - a_8^{2}\right| = 70$

$\left|a_8^{2} - a_1^{2}\right| = 80$

Determine the remainder obtained when $N$ is divided by $1000$ .

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-<math>8.</math> Let <math>N</math> denote the number of <math>8</math>-tuples <math>(a_1, a_2, \dots, a_8)</math> of real numbers such that <math>a_1 = 10</math> and
+==Problem==
+Let <math>N</math> denote the number of <math>8</math>-tuples <math>(a_1, a_2, \dots, a_8)</math> of real numbers such that <math>a_1 = 10</math> and
 <math>\left|a_1^{2} - a_2^{2}\right| = 10</math>
@@ Line 13: / Line 14: @@
 Determine the remainder obtained when <math>N</math> is divided by <math>1000</math>.
+==Solution==
+{{solution}}
+==See also==