# Difference between revisions of "1985 AIME Problems"

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==Problem 4== | ==Problem 4== | ||

+ | A small square is constructed inside a square of area 1 by dividing each side of the unit square into <math>n</math> equal parts, and then connecting the vertices to the division points closest to the opposite vertices. Find the value of <math>n</math> if the the area of the small square is exactly <math>\frac1{1985}</math>. | ||

+ | [[1985 AIME Problems/Problem 4 | Solution]] | ||

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==Problem 5== | ==Problem 5== | ||

## Revision as of 09:23, 3 December 2006

## Contents

## Problem 1

Let , and for let. Calculate the product .

## Problem 2

When a right triangle is rotated about one leg, the volume of the cone produced is . When the triangle is rotated about the other leg, the volume of the cone produced is . What is the length (in cm) of the hypotenuse of the triangle?

## Problem 3

Find if , , and are positive integers which satisfy , where .

## Problem 4

A small square is constructed inside a square of area 1 by dividing each side of the unit square into equal parts, and then connecting the vertices to the division points closest to the opposite vertices. Find the value of if the the area of the small square is exactly .