## September 14th, 2006

### eight queens boggler answered

[problem statement]
Monica explains:
When I was young I was taught the multiplication table. Fine. I waited for the other shoe to drop but noone ever taught me the "division table". So I figured it out myself by doing all the long divisions by hand (this was before calculators) and I memorized all fractions from 1/1 to 12/12 .

Decades later, I was teaching a data structures and algorithms class at my old univeristy. In the class book (probably Wirth's, but I'm not sure) was a complete listing of all solutions to the 8-queens problem expressed in a compact form as 8-digit numbers. One of them jumped out at me as containing the magic sequence "428571" which are the digits that form the expansion of 3/7 = 0.428571428571.. . .

So I quickly figured out it was 255 / 7 that gave us 36.428571 as a valid solution to the 8-queens problem. I was so fond of this discovery that I made it my corporate logo when I started Syntience Inc. in 2004.

### division table

I had reached the same conclusion some of you did in the comments on that last post and made myself a division table covering 1-12.

Some notes:
• It turns out that you already know most of them, and much of the rest follow patterns (like multiples of 1/12 cycle through multiples of 1/4 and 1/3 as you'd expect).
• I couldn't get pdflatex to generate landscape but I print postscript anyway so postscript it is!
• I keep imagining that after enough TeX and LaTeX it'll eventually start making sense to me (I broke down and read the TeXbook a while back), but in practice it remains about as obscure as it always has. This gives it the rare distinction of being more confusing and frustrating than even autotools.