Henry Ernest Dudeney/Puzzles and Curious Problems/345 - The Egg Cabinet

by : $345$

 * The Egg Cabinet
 * A man has a cabinet for holding birds' eggs.
 * There are $12$ drawers, and all -- except the first drawer, which holds the catalogue -- are divided into cells by intersecting wooden strips,
 * running the entire length or width of a drawer.
 * The number of cells in any drawer is greater than that of the drawer above.
 * The bottom drawer, No. $12$, has $12$ times as many cells as strips,
 * No. $11$ has $11$ times as many cells as strips, and so on.


 * Can you show how the drawers were divided -- how many cells and strips in each drawer?
 * Give the smallest possible number in each case.