For the record, I did actually work on it for a while. I usually ignore
these puzzle type things, but this one did catch my attention.
I got everything worked out except for the angles closest to x. It
seems to me that they should be solved via simultaneous (sp?) equations,
but I was unable to figure out what the equations should be. That's not
exactly elementary geometry, though, is it?
You can only do so much with caulk, cardboard, and duct tape.
To email me directly, send a message to puckdropper (at) fastmail.fm
I never was a whiz at math, but I did manage to struggle through 4
semesters of calculus and differential equations on the way to an
engineering degree. I spent several hours poring over this puzzle and
even drew it to scale on CAD. It was easy enough to measure the angle
by CAD and it turned out to be just what I had guessed it should be.
But the best I could do by following the rules was to reduce it to 3
equations with 3 unknowns. But I suspect my 3 equations are inbred
because I wasn't able to solve them. I don't believe it can be solved
by simple geometry alone.
"There's a difference between doing things right and doing the right
I drew a few contruction(deduction?) lines as per instructions (fused
into my memory) of the best math teacher ever (high school, The
Netherlands), he taught to be intuitive. I did solve it with geometry,
but in a long roundabout way. After I solved it, the obvious slapped
me in the face. I saw 'it'. I did end up feeling pretty proud of
myself, but admittedly after waaaaaay longer than I had first thought.
WAAAAY longer. I should have seen 'it' immediately. I didn't. Must be
That math teacher loved his job and subjects.
I had a salty dog, ex sailor, as a geography teacher in the same
school. When he talked about foreign lands, he had us all in the palm
of his hand. We could smell the products from far away places as he
described them. Annnnd, (stupid us, we didn't know ) he was teaching
all the while. To this day I enjoy learning new stuff about foreign
lands. OTOH, my biology teacher sucked canal water.
Ahh yes! Miss Anthony, 8th grade English, the impression she made on the
minds of us young lads, and the countless trips we made to worship her at
her desk ... and to peek down the front of her blouse.
The mammaries linger to this day!
I have not yet tried to solve it/them. No courage anymore.
My mathteacher was an elderly lady nicknamed koptelefoon, because of her
wound-up braids. Geography teachers were just weird. Biology teacher
was the greatest. I agree, slootwater can be really bad, but I did swim
in both the Rhine and Friesian canals. I also did other things, but
fishing was not my forte. Met my wife in '62 summercamp aboard this
My highschool math teacher was less than 5 ft tall and past 70 when
she tried to teach me.
Had a 48-49 Packard that when she drove, could barely see over the
steering wheel to drive.
Never did check to see if she ahd blockes attached to the pedeals so
she could reach them.
Had one who decided to check out one of her male students.
Suddenly, one day she was gone at noon.
Never really got the straight story, but then again, a small town in
the MidWest in the early 50s.
Pretty racey stuff for the period.
That's funny. We had a physic teacher we call
'drollevanger' (turdcatcher) because he wore those pants that puff up
at mid-calf height.
I went to sail camp the way kids go to regular camp every summer.
Indeed, the Friesian lakes, and the water was clear in the early
1960's. The Rhine, however, which ran through my home town Alphen aan
den Riin, was basically an open sewer. Much better now, but I knew
enough back then not to swim in there. The diverted Rhine, which now
flows through Rotterdam is down-stream from a lot of German
industry...not so sure I'd swim in it either.
Got to love those flatbottoms, eh? That's not the kind of sailing we
did. We sailed Rainbows:
(While looking for a picture of a regenboog, I saw what people are
paying for those these days...holy cow...)
I grew up in Wageningen, and the Rijn wasn't too clean, but
occasionally I'd swim there. Mostly if needed because the sailing boat
didn't stay up. The Rijn at Wageningen wasn't too crowded with
commercial traffic, but of course, we'd stay out of the way of the
Regenboog was an Olympic class from before WWII, I believe. Even when I
was a kid, they were rare because of their cost. Mostly BM'ers, maybe
Vrijheidjes (Freedom) and other even cheaper plywood boats. You know,
the kind for which daysailer was an exhalted term. Of course, glass and
plastic is the norm now. 30 years ago we got a present from people who
were moving cross country, a Snark. It was fun on the Charles in
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