While blog-hopping, I found an interesting math problem. My friend's sibling won a free math textbook for solving it the most quickly. The problem was this: Convert 0.151515... octal to decimal. After 20 minutes or so, I couldn't believe I hadn't reached the right answer yet and that it was taking so long for me to figure it out. I've been lingering--for quite some time now--on the belief that I've rapidly gotten dumber over the last year. And now, my inability to solve such a seemingly simple problem was proof of this. I kept on getting the same answer, that when converted back to octal became 0.115-something. No, that's not right, I said to myself. But then I carried it out a few more places and realized it was actually 0.11551155... I was closer than before, but I ultimately still had the wrong answer. I just wasn't able to solve it. (I should have realized what my error was at this point but that would have required real intelligence.)

It turns out I just made a careless calculation error. (I was somehow utterly convinced that 10₈ = 64₁₀ and not 8₁₀.) I ended up approaching the problem from a completely different angle (Method 2) and came up with the right answer in less than 5 minutes. But this story actually has a point. I think it was this conviction of stupidity that prevented me from spotting my careless mistake; instead, it led me to believe genuinely that I had become too dumb to come up with a viable method when, in fact, I had the right idea all along (Method 1). So I realize now that I'm not dumb--just rendered incompetent by carelessness. I guess I should just concentrate a little harder on being more careful instead of lambasting myself for lacking intelligence every opportunity I get. Now if each of my problems in life were as simply and elegantly solvable as this little math problem, things would just be so much easier.

solution: (highlight to read)
Method 1:	Method 2:
let x = (0.1515...)8 x = (15/(100-1))8, since it repeats every 2 digits x = (15/77)8 x = 158/778 x = 1310/6310 x = (13/63)10	let x be the solution, some rational decimal number with repeating decimal [a..] x = 0.[a..] 8x = 1.[b..], where [b..] is some other repeating decimal 8x-1 = 0.[b..] 8(8x-1) = 5.[a..], since it repeats every 2 digits 8(8x-1)-5 = 0.[a..] = x 64x-13 = x x = 13/63