A more thorough explanation can be found here: http://www.datagenetics.com/blog/december12014/index.html

If you look at the linked submission you'll see that the DataGenetics blog post is referenced. Personally, I found that to be too detailed in some parts, and not detailed enough in others - I felt it got the balance wrong. Of course, everyone's mileage will vary, but this intended audience for the item will tend to be more interested in the "NIM sum" than the XOR, even though they are the same thing. The "NIM sum" is what's used in mathematical games and puzzles, and will be familiar to the intended audience.

But again, YMMV, so you may prefer the DataGenetics version.

I enjoy both math and magic, and I especially enjoy puzzles like this that have an element of both. I wonder whether there happens to be any sort of positive correlation between the two disciplines. Are people who enjoy math more likely than the average person to also enjoy magic?

This is a nice lay-person explanation of hamming codes and how they're useful.

Interesting tidbit - it appears the universe uses them to preserve quantum state information. Make of that what you will.

> Interesting tidbit - it appears the universe uses them to preserve quantum state information. Make of that what you will

Huhwhat? I don't think that's true at all. Quantum states are continuous while Hamming codes are inherently discrete.

Have a read - it's interesting stuff - this is from Physics World - http://www.onbeing.org/program/uncovering-codes-reality/feat...

Ah, SUSY rather than QM. I think it's a bit much to say the universe appears to follow SUSY; it's been... not great at generating experimental predictions, and to the extent that there are results they are negative.

You just need such a interpretation for 16 bits, that swapping one out of 16 bits will be able to generate any number 0-15 for x % 16. Trivial really.

This puzzle is "flipping" awesome