MathDB

Let

w

and

h

be positive integers and define

N(w,h)

to be the number of ways of arranging

wh

people of distinct heights for a photoshoot in such a way that they form

w

columns of

h

people, with the people of each column sorted by height (i.e. shortest at the front, tallest at the back). Find the largest value of

N(w,h)

that divides

1008

Problem Statement