MathDB

Annie drew a rectangle and partitioned it into

n

rows and

k

columns with horizontal and vertical lines. Annie knows the area of the resulting

n \cdot k

little rectangles while Benny does not. Annie reveals the area of some of these small rectangles to Benny. Given

n

and

k

at least how many of the small rectangle’s areas did Annie have to reveal, if from the given information Benny can determine the areas of all the

n \cdot k

little rectangles? For example in the case

n = 3

and

k = 4

revealing the areas of the

10

small rectangles if enough information to find the areas of the remaining two little rectangles. https://cdn.artofproblemsolving.com/attachments/b/1/c4b6e0ab6ba50068ced09d2a6fe51e24dd096a.png

Problem Statement