Talk:Henry Ernest Dudeney/Modern Puzzles/168 - The Magisterial Bench/Solution

By applying the Inclusion-Exclusion Principle, I got:
 * $10! - 9! \times 2 \times 3 + 8! \times 2^2 \times 3 - 7! \times 2^3 = 1 \, 895 \, 040$

and a program I wrote confirms this, but I would like a second opinion (as is the case for most combinatorics stuff). --RandomUndergrad (talk) 05:58, 13 February 2022 (UTC)


 * I must have been really tired or drunk or something when I wrote the original solution to this. I turned over the page to discover I had read only part way through Dudeney's solution in his Modern Puzzles, thinking he had finished everything he had to say at his first invocation of $443 \, 520$.


 * I've redone it now, and I have his complete solution in place.


 * Please feel free to add your own exposition which will arrive neatly at the application of Inclusion-Exclusion Principle, and implement it as Proof 2. All the infrastructure is in place. --prime mover (talk) 22:10, 18 February 2022 (UTC)