How to draw a combinations tree -- tree diagram for combinations

I've been working on basic Algebra II concepts recently, especially tree diagrams for combinations and permutations. Permutations are relatively straightforward, but not combinations. So, I asked a question on, and although I never received a response, I think that my sketch, shown below, is roughly accurate:

Simple, Fast Way to Enter/Type Unicode Characters in Windows (using UTF-8)

I often need to enter the International Phonetic Association's (IPA) or other math symbols into my computer, often during a lecture, when speed matters. Some great webpages, particularly this one, explain how, but they require you to know the Unicode code numbers. That is far too cumbersome for me. My approach is a little different, and much more intuitive.

Enter Unicode characters using AutoHotKey (AHK)

  1. Download AutoHotKey (free)

Convert IPA Symbols to Speech Sounds Online (MP3)

For a long time, I had been curious what an IPA to speech sounds / MP3 audio converter would sound like. Google doesn't list any free tools. So today, I wrote a free converter in Python. The code is extremely basic and not a good example of programming, but it does illustrate the point of why so few converters probably exist: the results are nearly worthless--at least, when using such simple logic (i.e., just play each IPA sound in order as transcribed).

Nitro PDF (the free version) fixes Acrobat Could Not Save error 18

As explained here (, NitroPDF can fix some broken PDF files. In my case, Acrobat Pro XI refused to save a PDF file, saying it had error 18. After reading that previous tip (which saved the file normally but didn't fix my problem), I opened the file in Nitro PDF, then clicked File -> Save as -> Flattened PDF instead, and voilà, the PDF worked normally again! Yay!

Simple, Easy, and Free: Black background for OneNote 2010, OneNote 2013, and OneNote 2016 (no junkware/spyware)

If you'd like a black background for OneNote, you can buy OneNote Gem (which is fantastic), or you can download a free OneNote 2010/2013 formatted section whose background is already black. You just double-click the file, OneNote will load, and open a new section whose only content is a new page with a black background. Yay!

Sage / SageMath: TI-84 / TI-89 Split Screen

Lately, I've been learning the basics of Sage (SageMath). Today, I wanted the equivalent of the TI-84 or TI-89 "split screen" feature with a graph and table of values side-by-side. Here's my attempt: SAGE CODE
x = var('x')
f(x) = x^3
coords = [(i, f(i)) for i in [-3..3]]

Contrarily vs Contrary

As I posted in WordReference (, here is an explanation of Contrarily vs Contrary:

English to French: not x years ago, ...

If you'd ever wondered how to translate "Not x years ago, y happened" or "Not x minutes ago, y happened" it seems that "encore" might do the trick, as I write on a post: I may have found an answer. In its entry for "encore," Oxford Superlex writes: "7. (seulement) only, just; il était pratiquement inconnu il y a encore trois mois he was practically unknown only ou just three months ago." and wrote the following:

OneNote 2013 microphone (mic) not working - Microphone Muted intermittently

If OneNote 2013 is not recording consistently (i.e., inconsistently recording or OneNote 2013 recording is just not working) on your Surface Pro 3 (mine is 256GB with OneNote 2013 Retail (Academic) version), then you're not alone (see this post at Microsoft:

Anymore vs Any more -- What's the difference?

The difference between anymore (one word) and "any more" (two words) is described by Huddleston, Pullum, and Bauer in the Cambridge Grammar of the English Language as follows:

NPI: Negatively-oriented polarity-sensitive items
PPI: Positively-oriented polarity-sensitive items

anymore is an NPI: The any class of items: any, anybody, any longer, any more (AmE anymore), anyone, anything, anywhere


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