Henry Ernest Dudeney/Modern Puzzles/102 - The Nine Barrels

by : $102$

 * The Nine Barrels
 * In how many different ways may these nine barrels be arranged in three tiers of three
 * so that no barrel shall have a smaller number than its own below it or to the right of it?
 * The first correct arrangement that will occur to you is $1 \ 2 \ 3$ at the top then $4 \ 5 \ 6$ in the second row, and $7 \ 8 \ 9$ at the bottom,
 * and my sketch gives a second arrangement.
 * How many are there altogether?


 * Dudeney-Modern-Puzzles-102-question.png