Challenge Questions

looks like a snowman with some parts missing.

Customers must buy accessories separately.....

Must be because I didn't quite keep a square matrix.

Fyz

I know, unit .

You'd need to be a doughnut to to think any of those are straight lines:-

But, I suppose I have to admit they're worth a Good Answer.

LOL - and ta for the GA.

That doughnut is doh'ing my nut in ! Having the wire wrapped at angle looks like a dodgy bit of deception to suggest 1 loop. Your drawing is clearly better than mine - if you add to that picture, there's a good chance of getting a GA from me.

Where's the joke? (and that illustration looks like an exact inverted copy of #6)

It Is! but the dots are the not inverted.

He he (there are no dots)

Oh.... Circles!!

The dots inside the circles are to small to see. He said they were real small.

Try TurboCad LE (TurboCad Learning Edition): this free download (just click on the bulleted item at the top of the linked URL) includes a 271 page book. Although this is only version 4 (TurboCAD is now up to version 16), it includes everything that a casual user would use in a 2D cad package.

IMSI (who make TurboCad) also now do a much more comprehensive 2D CAD called DoubleCAD. It's got the look and feel of AutoCAD lite, but with some of the better features of TurboCAD: you can get it free from CADcourse (it's a dollar with a dollar discount; you don't need to enter your credit card details or anything and they haven't bombarded me with spam).

For a more mathematical package try GeoGebra (sorry to give away one of your secrets Kris), also free.

When you've done your drawing: do a screen capture; save as a .jpg file, and, insert into the CR4 editor using the little green camera above the editing screen.

Click on browse and find the picture on your computer.

Sparky did a great little tutorial on inserting graphics some time ago.

he he....no big secret, I've mentioned it enough. Not as fancy as the others, but cool for Euclidean play.

Tricky, but doable.

Here's one that plagued us during those dark days pre-WWII in general physics lab. Mr. Lariton promised a final grade of 100% without taking the final exam to anyone who could solve the puzzle.

There are three blocks representing three houses. In front of each house is a utility hook-up.

The problem is to run a line from each utility hook-up to each house without crossing any lines.

No one could do it, but no one flunked his course either.

He then revealed to all of us at the end of the semester that there is no solution the way the problem is presented.

Is there a solution?

Ken Leigh

It's an oldie, but good. That site is a neat one, though I first saw the problem some place I've long forgot. "Riddles In Mathematics" (Eugene P Northrop) is a fun read, though I'm not sure if it's still in print.

You can do it by taking one of the lines through one of the houses or through one of the utilities. You can also do it by placing all the buildings on the surface of a doughnut, but, that really only amounts to taking one utility under or over one of the others, which is of course what happens in the real world.

To prove that it can't be done without cheating, you need to look at the way loops divide up a simple 2D space. I know that Fyz will say that this is not rigorous, but it "works for me".

First lets have a stab at the problem:-

I've got in all the lines except 2 to B. (I could "cheat" at this point and take a line through A). Let's take out some of the lines and simplify the drawing a bit:-

First look at the loop 1,A,3,C,1

It divides "the world" into two areas: an inside, and, an outside.

It doesn't matter whether we put B inside or outside, once we connect up 1,B,3 we have sub divided one of those two areas into two more distinct areas. In this case I've put B inside the original "loop", but I think you can see that it doesn't matter which I chose.

Now the world is divided into three areas. If we put 2 outside the original area it is isolated from B; if we put 2 in the loop 1,A,3,B,1 it is isolated from C, and, if we put 2 in the loop 1,B,3,C,1 it is isolated from A.

As I said not rigorous, but, a basis on which a "reasonable" person could argue that the original problem is impossible.

I see that Kris has beaten me to this with a link to a more more formal solution.

I think your proof is a well-chosen subset of the full proof. The missing bits probably aren't worth knowing about (except for those who want all the i's crossed as well as dotted)

To: Physicist

Makes sense(?) to me. As I recall, Mr. Lariton used a similar concept when he showed us that a solution was impossible.

That did not mean that thirty-three students (of which I was one) didn't try that whole spring to solve it.

Of course, none of us did, but Barb H and myself determined early on that it was impossible to solve, for which Mr. Lariton gave us a "passing" grade of 95% (after we took the final exam!), the lowest grade I received that year. It brought my average down enough so that I was merely third in a class of eighty-six instead of first!

Ah, yes, I was a smart ass then, and haven't changed one iota since!

You know what they say, gals and guys, once a smart ass, always a smart ass, or, everyone likes ass, but no one likes a smart ass, or, you can always tell a smart ass, but you can't tell them much!

Oh, BTW, what do you call a retarded lawyer?

Ken Leigh

The old ones are still good.
It depends on the level of retardation. Full-scale (in the UK) would be "My Lord".