MathDB

A small square is constructed inside a square of area 1 by dividing each side of the unit square into

n

equal parts, and then connecting the vertices to the division points closest to the opposite vertices. Find the value of

n

if the the area of the small square is exactly 1/1985. [asy] size(200); pair A=(0,1), B=(1,1), C=(1,0), D=origin; draw(A--B--C--D--A--(1,1/6)); draw(C--(0,5/6)^^B--(1/6,0)^^D--(5/6,1)); pair point=( 0.5 , 0.5 ); //label("

A

", A, dir(point--A)); //label("

B

", B, dir(point--B)); //label("

C

", C, dir(point--C)); //label("

D

", D, dir(point--D)); label("

1/n

", (11/12,1), N, fontsize(9));[/asy]

Problem Statement