A Theorem about Primes Proved on a Chessboard | Hacker News Reader

A Theorem about Primes Proved on a Chessboard

fermatslibrary.com

99 pointsluisb14 comments

This reminds me of a boardgame, played with 8 queens on a chess board, that was part of the National Mathematical Games Championship when I was in high school (in Portugal). It's called Game of the Amazons [1], and each player owns 4 queens. They take turns moving one of their queens to a valid position and then placing a stone within "sight" of this queen. Stones block cells and the first player to not be able to move any of his queens loses. Quite dynamic, and fun to devise successful strategies.

Cool paper by the way!

[1] https://en.wikipedia.org/wiki/Game_of_the_Amazons

I played this in College! It was my AI final, each team had to program an AI for this game and then on the last day of classes we pitted our AI's against each other. It was a ton of fun, and taught me a hell of a lot about functional programming and some fancy data structures.

I never heard about this kind of game. So to summarize (if I understood correctly), this would be a variation of the classical 8 queens problem [0] but on a wider board. Very interesting !

[0] https://en.wikipedia.org/wiki/Eight_queens_puzzle

It is a little more complicated because the queens move around from turn to turn, they shoot "arrows" to block each other's movements, and they are not forbidden from being in a position to attack one another in the chess sense. Those aren't features of the traditional eight queens problem. (I haven't played the game, I just read the rules online.)

This is a nifty paper. Also very cool is the proof without words that just happened to be in the same journal page as the last part of this paper.

Why are those sequences equal? Does it generalize, or is it just a coincidence.

yeah, that was a very pleasant surprise

Loren C. Larson; Mathematics Magazine Vol. 50, No. 2 (Mar., 1977), pp. 69-74

Why do sites insist on doing stupid things with scrolling?

The mouse scroll wheel doesn't work, there's no scrollbar, page up/down don't work, arrow keys don't work. WTF? Just use the regular built-in scrolling. I didn't visit the website to spend 15 minutes figuring out how to navigate it.

> Why do sites insist on doing stupid things with scrolling?

One possible reason is: testing only smartphones and tablets.

I don't see that problem with this site, though. There is a scroll bar and the wheel works for me (FireFox 48.0.1). I allowed JavaScript from mathajax.com and from the site itself (fermatslibrary.com), but not Google Analytics.

However, a modal dialog box pops up about subscribing to the newsletter. Scrolling doesn't work until it is dismissed. HYPOTHESIS: if that dialog is somehow mispositioned off-screen, it will look like scrolling is busted.

For me, that dialog pops up after the passage of some number of seconds after a full reload of the page. It tracks the position of the lower right corner of the browser as I resize; I can't get that dialog to go off-screen unless I shrink the window ridiculously so it goes above the top edge or past the left edge.

> a modal dialog box pops up about subscribing to the newsletter

I was wondering why I had the site marked as untrusted to execute javascript. That answers that.

Ah, I feel silly now, it looks like I caused this. At some point I must have added an adblock rule to block the subscribe dialog on fermatslibrary.com, but somehow missed the disable scrolling part.

I just clicked the link again and was able to scroll for a few seconds before it stopped. I toggled ad-block and the subscribe box became visible.

Earlier, I opened the page in a new tab and didn't get to it for a while, so when I switched over to read it, the subscribe box had already disabled scrolling.

All of those things work perfectly normally for me.

It works fine for me -- I have Javascript disabled by default :P

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