# Super stalemate

Yesterday I posed the following puzzle: is stalemate possible in chess if it is legal to move into check? Give it some thought first, then see my answer below.

# A chess variant puzzle

Consider the rules of chess modified so that the objective is to capture the opposing king. (I once played someone who apparently thought this was the objective, which was my inspiration for this.) The rest of the game remains the same, except that it is now legal to move into check—otherwise capturing the king is impossible, since checkmate would be followed by stalemate.

At first glance one might think the game is identical so long as one takes care to never move into check if at all possible. In fact, the game has appreciably changed since forcing a stalemate is harder when one has additional legal moves.

The puzzle is this: is stalemate even possible now? Why or why not?

# Cute problem solution

Yesterday I posed the following problem: If $S$ is the set of positive integers whose decimal expansion does not contain a 3, does

$\sum_{n\in S}\frac{1}{n}$

converge or diverge? My solution is after the break.

# Cute math problem

Here’s a quick math problem to think about. Let $S$ be the set of positive integers which do not contain a 3 when written in decimal. Does the sum of the reciprocals of the numbers in $S$ converge or diverge? I’ll post my answer in the next day or two.

# First post

So I took the plunge and decided to start up a blog, primarily as a way practising writing, something I’ve always enjoyed but never made a habit out of. I read a fair number of blogs, but to be honest I wouldn’t miss most of them if they shut down. I’ve found a few which consistently produce high-quality content; here are three of my favourites:

• Paul Graham – A fantastic collection of essays. I like Graham’s writing style more than anyone else I’ve ever read, and don’t understand why the clear, matter-of-fact style that he employs isn’t very commonly used. Many of his essays are about entrepreneurship, which I am not especially interested in, yet I still find his writing engaging.
• Scott Adams – Best known as the creator of Dilbert, his blog is a constant source of unique ideas. As a compulsive thinker who loves kicking around new ideas I look forward to reading his near-daily posts.
• Eric Raymond – An open-source software advocate with an extremely strong ego. The unusual part about that is he actually has the accomplishments to back it up. He writes about a diverse number of things, and his writing is usually interesting even when I don’t care much about the topic.

My intention when starting this blog was to only write about things of interest to me. I had thought that this would necessitate being boring to everyone except in the case where a common interest is shared. Judging from the above list, in the optimal case that’s not actually true.