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Find all integers $N$ such that $N^2-71$ is divisible by $7N+55$ .

What is the greatest integer k such that 2^k is a factor of 67! ?

A boy has 3 pairs of trousers, 2 jackets, and 5 shirts. How many different combinations of trousers, jackets, and shirts can he put together?

Points A, B, C, D are on a line such that AB = 3, BC = 6, CD = 8, and DE = 4. What is the smallest possible value of AE?

A polygon is a closed figure whose sides are straight lines. The above figure shows a six-sided polygon (a hexagon). Show that the sum of the angles of a hexagon, $S^o$, is $S^o= 540^o$.

Then, show that the generalized formula for the sum of the angles of an n-sided polygon is $S^o= 180^o(n-2)$.