Puzzle

Another hard one from the problem-a-day calendar.

My officemate and I discussed this one on-and-off throughout the day, drawing and redrawing many extra lines and triangles. We did finally solve it, but by a kind of questionable meta-method. Here's the basic idea:

Imagine blowing up the circle just a little bit. The line on the left can still be 12 units long. It will still be possible to have another line cut a chord 7 units long. And it will still be possible to have those two lines meet at a point. The angle they form will be different, though, and the value of x may be different. But the angle isn't a given and neither is the diameter of the circle. Therefore that problem is the same problem as this one. Since we know this puzzle has a unique solution, the value of x must actually be a constant and we can make that angle whatever we want. We will make it such that the chord is actually a diameter.

From that point the puzzle is easy and this method did yield the correct answer. The questionable part is assuming there was a unique solution. If we had come across this puzzle "in the wild" this wouldn't have been at all kosher. So how did the first person solve this puzzle? What's the real solution?

I Did It!

• Woooo! On 03/26/2007 I started at 259. Today I'm at 199.

  That's right, just 1/2 lb per week. Slow and steady catches the worm. In graphical form:

  My BMI is still technically overweight, though. Granted, BMI isn't a very good measure, but in this case I agree with the assessment and I'm going to go for 10 more lbs.



• I've only recently started using multiple colors of clay together. I have an irrational fear of "using up" the clay when I mix it, even though a pound of clay is like $1. However, a clay model gathers impossible-to-remove dust and small nicks. So I've finally bitten the more expensive bullet of switching to sculpey.

  A 4 year old of my acquaintance calls this "the treasure cat" and a 2 year old, also of my acquaintance, calls it "measure cat". (Also, any Cheshire Experts will notice right away the wrong color I didn't notice until too late.)



• I have a scrollsaw from way back but the blade broke and it turns out that that size is hard to find. Then last weekend I found a bandsaw at the flea market! After some tuning and tweaking, it's running great.

  Is this

  the first step on the road to this?

  Doubtful. But maybe!