Joe
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 Jan12 comment Is it true that the Fibonacci sequence has the remainders when divided by 3 repeating? If (0,0) were visited, wouldn't that mean it would always be 0? Seems that segment must never be visited (assuming you don't start a similar sequence with two multiples of 3). Dec19 awarded Caucus Dec19 awarded Constituent Dec15 awarded Autobiographer Aug27 comment What is the average of no numbers? I agree that 0 is a sane choice if it needs to be defined - and in practical scenarios, it might need to be. I would also suggest that if you are taking a mean of something with a known or expected population mean, some other value might be a good default to choose, such as said expected mean. Imputation basically works this way - when NaN doesn't suffice, and you need a point for each day, picking a point that makes sense with the other points is a reasonable choice.' Jan10 comment An oddity in some linear equations Sort of like a binary tree, logically speaking. At the point in which you consider dividing by $x$, what you really do is have a node with two branches. if x≠0 then [divide by x] and if x=0 then [cannot divide by x]. You traverse the first branch, and end up with an absurdity; so that means you know the second branch is the correct branch, at which point you've solved the problem. Jan7 comment Pedagogy: How to cure students of the “law of universal linearity”? I actually find it easier to explain $(x+3)(x+3) = (x+3)*x + (x+3)*3$. IE, treating the _first_ $(x+3)$ term as a single unit, it becomes identical to $y(x+3)$, which then is easier to understand as $y*x + y*3$. Jan7 awarded Teacher Jan7 answered Pedagogy: How to cure students of the “law of universal linearity”? Dec17 comment Monty hall problem extended. No Monty Hall question is complete without someone disagreeing with the (well established) answer. Feb22 awarded Supporter Feb22 comment What's next in this number series? I came to the same answer independently; i'll say that my thought process was, 'Hmm, 340x2=680, I wonder if there is a relationship between 680 and 1428 - yep, 2.1...' and then just verified the rest. This is the sort of test they use to see if you have second-order thinking skills, so it is always a second degree relationship.