I saw this in today's Financial Times. I think it's a pretty cute puzzle, and I think I know what's up, although I have not yet checked.

Anybody care to explain how 64 became 65?

If you know the answer, don't post it here. Send it to me. After a few days I'll post the winner's explanation. This way it won't get spoiled by the first one.

This message has been edited. Last edited by: Pete Riegel,

That's easy.

The rectangle is the original shape, and it was cut with a wide blade. When reassembled as a square, one unit was "lost" but it's really a pile of sawdust on the floor.

At least that's how I'd explain it.

I'll take a stab, as my first post on site. (I haven't measured a thing yet, but hope to play with my "inherited" Jones Counter soon.)

The fallacy is the assumption that the square equals the rectangle. It doesn't. The smaller angle of the triangle and the angle adjacent to the larger trapezoid leg, add up to a bit LESS than 90 degrees. If one rearranges the pieces of the square (as I did in Visio), there is a noticable gap between the two large "triangles."
(This gap, aperture, whatever, looks like the slit of a cat's eye!)

Actually, an easy way to confirm it is, the angle of the original small triangle with legs of 3 and 8 is arcsin 3/8, or a hair over 22 degrees. The angle in the large triagle in the rectangle, is arcsin 5/13, or 22.6+ degrees.

I bet the area of this slip is equal to exactly one square unit.

And if I figured out how to save pictures on a remote server, I'd post the "plane figures" (plain facts?) I built in Visio.

As I do my first cal course before my first race course, I'm sure I'll have other questions for elsewhere on the board.

Best regards,

Rick Cronise

This message has been edited. Last edited by: Rick Cronise,

Here’s the puzzle answer from yesterday’s Financial Times.

Mark Neal came in with the first correct answer, followed by Mike Sandford and Rick Cronise.

The trick to the puzzle is to realize that the right-hand view in the original puzzle is not correct. The angles don’t match up to make things fit.

I saw this puzzle, when I was in high school. I graduated from high school in 1961.

Dale Summers

I bet Pythagoras saw it when he was in HS, too.