I took *The Art of Computer Progamming Volume 4, Fascicle 0: Introduction to Combinatorial Algorithms and Boolean Functions* home last night to read instead of my usual, the dragon compilers book. AOCP Vol 4 Fas 0 is all about graphs and combinatorial puzzles. The book starts off with Knuth talking enthusiastically about how much he loves combinatorial problems, and the first chapter starts off with a couple of historical combinatorial puzzles. I’m not usually into puzzles, but these were actually so much fun.

##### Langford pairs

You are given the numbers {1, 1, 2, 2, …, *n*, *n*}, and you want to place them in a row so that exactly *k* numbers occur between the two appearances of each digit *k*.

When *n* = 3, there is essentially one way to arrange them: 231213 (and it’s left-right reversal)

What is the solution for *n* = 4?

##### Card sudoku

“Take all the aces, kings, queens, and jacks from an ordinary deck of playing cards and arrange them in a square so that each row and each column contains all four values and all four suits.” - *Recreations mathematiques et physiques* (Paris: 1725, Jacques Ozanam)

I hunger for more puzzles!