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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

Only a touch, I reckon.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,665

I remember a movie called "Quigley Down Under." There apparently were a lot of cowboys in Australia. I guess they brought the expression, "I reckon."

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

Ah reckon ye'd be bang on there.

*Last edited by phrontister (2012-10-25 01:18:39)*

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,665

That is it. Seems that a while back some Texans got lost, took a wrong turn and ended up in Australia.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

And they're very hard to tolerate, too.

Overheard a couple of 'em the other day, with one who'd been here before briefing the other one on what to expect:

"They're OK, these Aussies, but you'll find they take themselves a bit too seriously sometimes, so you'll have to humor them.

"For instance, if they say that Australia is bigger than Texas, you just make out you believe 'em!"

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,665

Yep, those are Texans alright.

I am going to get some sleep see you later and thanks for working on the problem.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

Sleep well...I enjoyed the problem.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

Hi Bobby,

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,665

Hi phrontister;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

Hi Bobby,

Here's an image of the first 29 rows of my Excel solution, including most formulas.

You used M, I suppose. I haven't put any thought into attempting an M solution as E & LB are still my go-to solving programs, and I haven't tried much to shake the habit.

*Last edited by phrontister (2012-10-30 01:46:29)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,665

Hi phrontister;

I used geogebra to give me a solution that M could work on. Thanks for supplying your method.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

Hi Bobby,

The answer in my first post (#1552) was from a drawing I did in Word.

I didn't mind doing it by 'hand' then because I'd mistakenly thought there were only a few rectangles, having scaled them to 100th their correct size in relation to the triangle. That accounts for the fact that my correct answer turned out to be about 100 times greater than my first.

So I was actually quite close - mainly just a couple of zeros missing from the end, that's all...which is nothing.

But you know what they say...

*Last edited by phrontister (2012-10-26 02:15:33)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,665

Hi;

Originally I was trying to get geogebra to draw the rectangles for me, layer by layer. Then it became obvious that was not necessary and an M solution took shape.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

Hi Bobby,

I actually started placing the tiny rectangles into the triangle in Word (at 500% magnification and with automatic object alignment) and got as far as about 10 rows - which took a while. I stopped when I realised that the answer might depend on which triangle side I ran the rectangles parallel to, and couldn't picture myself still busily placing little rectangles carefully into a triangle into my old age.

That's when I thought I'd better try to do this properly and with better accuracy, and came up with the Excel idea.

Would you like to show me your M solution, or at least give me a good hint? I haven't got a clue right now as to how to do it in M.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

It's bed time for me now - way past it, actually (again) - so I'd better sign off before I nod off.

See you later, Bobby.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,665

Hi;

Okay, have a good night. See you tomorrow.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

Hi Bobby,

is my code in LB.

It's a bit wordy, but if I look at this post in 50 years' time it'll be easy to work out what I did.

*Last edited by phrontister (2012-10-31 11:14:34)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,665

Hi phrontister;

That is nice, neat code. Hope you will give it a try in M.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

Hi Bobby,

Ok...I'll try, but not sure when. Off to work now...

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,665

Hi;

Very good, if you need help...

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

Hi Bobby,

Lines 4 & 6 are repeats of line 2. How do I steer the third and fifth lines into the line 2 calculation route so that I can eliminate lines 4 & 6?

*Last edited by phrontister (2012-10-29 00:50:00)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,665

Hi phrontister;

I am the worst in the world at debugging or streamlining someone else's code but I will look at it.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

Thanks, but take your time, Bobby.

I have a very early start in the morning, so it's bedtime for me now.

See you later...

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,665

Hi;

Line 5 is different than line 3, can you make it the same. I am talking about

h = IntegerPart[250*150/b];

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

Hi Bobby,

Line 5's h (ie, h being the height from the base of side 50√34) has to be calculated as it's not given (unlike with the other two orientations of the triangle). In LB & E I got them to do that calculation of h, and so that's what I did in M's line 5. The integer part of the height is 128, so the h equation in line 5 could read "h = 128", instead of the formula for h.

But that's not the issue (although maybe you've got something up your sleeve that prompted you to ask me that question).

Lines 1, 3 & 5 contain different information as they pertain to the three orientations of the triangle, with each side taking its turn at being the base. Each of those lines is followed by a line (2, 4 and 6 respectively) that calculates the preceding line's maximum number of blocks.

In LB I was able to dispense with lines 4 and 6 by using GOSUB and RETURN and directing the calculation for each of lines 1, 3 & 5 to be done by line 2. However, in M I had to copy/paste line 2 twice to give lines 3 and 5 their own calculation lines as I couldn't work out how to direct them to line 2 to get their calculations done there.

That was the quick 'n easy way and gets the job done, but it left me with the question I couldn't solve.

*Last edited by phrontister (2012-10-29 19:44:21)*

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