And indeed you should. (And obviously you can use some other permutation -- change the second digit of the first number and the first of the second; the fourth digit of the third number and the third of the fourth; etc. Or whatever.)
An observation not always made: the diagonal argument, if you write your numbers in binary, is basically the same thing as Russell's paradox. Think of each number as defining a set of numbers -- the positions where there's a 1. The number we're constructing also corresponds to a set of numbers. "The nth digit is different from the nth number" says "n is in our set iff n isn't in the set labelled n".
If there were only countably many sets of positive integers, then we could label our sets with themselves instead of with the numbers 1,2,..., and then the new set we constructed would contain n iff set n doesn't contain n; that is, it would contain each set iff that set doesn't contain itself; this is exactly what Russell does.
Except that he does it with all sets rather than just sets of positive integers, and so what he proves in effect is that if we think we have a "universe" of all sets then we have to be wrong because here's a way of finding a new one.
I would like to use the Quinaplus Matcher to look for words that are made from two letter sets, let's call them $word_a$ and $word_b$.
The letters in $word_a$ can be in any order, and between $1$ and $n-1$ from $word_b$ in front and enter remaining $n-1$ to $1$ words behind.
E.g. if $word_a$ was ...
You are playing the classic game of 3x3 Tic-Tac-Toe. You are blindfolded and you cannot see the grid, while your opponent can see it. When making a move you call out a cell. If that cell is taken you are told that it is taken and you can call out another cell until you find an empty one. You make...
The idea of 'turning around' was conjured up, although I guess usually a rotisserie is more a cyclical thing than a reversal per se... I see why you say it wasn't necessarily 'fair' in that regard!
I figured that _I_ was part of the wordplay, so the definition had to come first. Thinking of 5-letter synonyms for 'cooks' soon led me down the right path :)
Describe can mean to trace out (Jupiter describes an ellipse around the sun), though that's not quite what we need. I'm not sure why I've seen it used as a containment indicator, but I know I have.
"Hi Pat."
"Did you get the proposed trip I sent over? Better book soon, because this big-city tour is going fast!"
"Well, if this is the route map you want me to choose from, I don't think this airline is going to be in business very long. Seattle must be one of the worst cities in America to hav...
@Tacoタコス It's not. I omitted the punctuation because I wasn't sure what to put. "Who knows" in this (surface) context is a statement rather than a question, but is usually punctuated with a question mark nonetheless. But I didn't want to end my clue with a question mark, because that has a connotation in cryptic clues that I didn't want to impart.
(Also, because it's a statement rather than a question, I didn't feel bad about omitting the question mark.)
My thoughts jump to CONTEMPORARY (stylish) with CON+TEMPORARY, but I can't think of a way to equate 'for sure' to CON, so it's probably not the intention...
ANTIQUARIANS would fit perhaps? It's not technically a style, but I think you can call somebody that in reference to appearance (i.e. being antiquated) and the plural for the hobby...
Polanski's magnificent Chinatown (my all-time fourth favourite film) was produced among numerous other movies by Robert Evans, the second anniversary of whose death is today1.
What better excuse for a commemorative brainteaser in the form of a matchstick puzzle?
Move four matches to turn CINEMAT...
It was a typical Sunday morning: coffee in the sun room, me and the paper, the wife and her phone. But this day as I read, I became increasingly aware of the wife’s good mood. She was humming, swaying, and tapping away on her phone like I never saw before. I’m not a jealous or suspicious man but ...
I don't know why I even took this class. All the math is so complicated. We were learning order of operations and then I get this monstrosity. Can you help me do it?
$(3+4)(2-3)=18-1$
$(2-7)^2+(1+5)=-44-33$
$(5-1)(9+8)=53+31$
$(6-2)^2-(10-13)= \ ?$
I am thinking about this question:
The public solution is
But I think I have another working solution, but I wasn't able to find any validation.
I think it's
Did I miss anything or is this also a valid solution?