plonq: (Studious Mood)
I grabbed a book of brain teasers as I crawled into bed last night and glanced at the first couple of puzzles in the book.  The first two were pretty easy word problems in the "find a word that contains the letters wkw in that order" vein.  The third problem in the book, however, involved creating a magic square.

It may astound some of you know learn that I have never actually tried this before last night.

If you're not familiar with a magic square, it's a 3x3 grid into which you insert the numbers 1 through 9 in such a way that the sum of the digits is 15 in all directions.  The book said, "You could do this by trial and error, but it would be more fun if you could come up with some rules in building the magic square."

I decided that an even better challenge would be to develop the rules and construct the magic square in my head.  It turns out that it wasn't nearly as hard as I'd thought it would be.

My solution is behind a cut in case you want to try it for yourself first. )
plonq: (Angelic Mood)
Assume         a = b
therefore      a - b = 0
additionally  2a - 2b = 0
therefore      a - b = 2a - 2b, or
             1(a - b) = 2(a - b)

Now if we factor out the (a - b) from this equation...
                1          1             1(a - b) = 2(a - b)                -----------------                    (a - b)                       1 Ergo          1 = 2


Most people spot the fallacy right away, but it's surprising how many people I've caught with this one.

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