I've found this to be INTERESTING..

LQ · 2010-02-21 08:12:51

Reality has hurt in repetition, that is why a problem may or may not be painful to solve or hear the answer too.
I'd say do both, that way you don't have to do the same thing twice. Good Luck.

phrontister · 2010-02-21 09:51:31

Btw, the formula I gave in post #21 was simply derived from observations that I made from a list of results produced with x,y values ranging from -100 to 100 for each variable.

I used BASIC to find x,y answers within that range that satisfied ZHero's "X*Y is congruent to X+Y mod 9" problem and then printed the list.

Last edited by phrontister (2010-02-22 00:49:05)

bobbym · 2010-02-21 09:59:42

Hi phrontister;

Sorry, I didn't get around to looking at your stuff because I am busy with Ricky. Excuse me my friend, but I am exhausted and need some rest. Sorry for that. Will look at it when I am awake.

phrontister · 2010-02-21 10:04:13

Sleep well. No rush...I'm off to work now. Maybe when I get back home I'll check out that 'digital root' option some more.

bobbym · 2010-02-21 22:40:21

Hi phrontister;

You are correct. But you didn't have to check further than 0 to 8 because of the mod 9 aspect of this problem. See my answers in post #8 and mathsypersons program for a procedural approach that can easily be converted to Basic. You can change his <=9's to <9.

phrontister · 2010-02-22 01:26:48

Hi Bobby,

The 'digital root' option didn't work out, and so I've deleted reference to it.

But you didn't have to check further than 0 to 8 because of the mod 9 aspect of this problem.

Oh, yes...I see. I hadn't understood that point until now.

I think

is much the same as mathsyperson's.

I had to remove negative test numbers from my original program because I was getting incorrect mod results (eg, that -14 mod 9 = -5, instead of 4); and I didn't know how to fix that without too much messing around that I shouldn't have to do. Excel did it correctly (answer 4...same as WolframAlpha).

My output table of solutions and their remainders made it easy to analyse and work out the formula that I mentioned earlier. Testing x,y = 0 to 100 made the pattern obvious.

Last edited by phrontister (2010-02-22 04:35:26)

bobbym · 2010-02-22 04:23:34

Hi phrontister;

If you look at the range of his inner loop you will see that he is making use of the fact that x + y = y + x and xy = yx. In other words for any answer (a , b ) then (b , a) is also a solution.

phrontister · 2010-02-22 04:40:24

Thanks, Bobby...I'd overlooked that. I've changed the code and output in my previous post.

Little touches like that of mathsyperson's I like a lot! But I usually miss thinking of them myself.

bobbym · 2010-02-22 05:01:15

Yes, he is very gifted. I am also impressed with how quickly you pick things up.

phrontister · 2010-02-22 19:29:51

Hi Bobby,

I am also impressed with how quickly you pick things up.

What you may not be aware of is that during the 16 minutes and 50 seconds that it took me to reply to your post I made and drank a hot cup of tea even before reading what you wrote. I also typed my post one-handed with one finger, as it was early morning here and my other hand was fast asleep. So was most of the rest of me...except for my brain, which was barely ticking along on autopilot just pre-bedtime.

bobbym · 2010-02-23 09:14:44

I also typed my post one-handed with one finger,

So, you took that speed typing course. I got take that one day.

phrontister · 2010-02-23 09:33:11

bobbym wrote:

So, you took that speed typing course.

Nothing to do with typing speed...

bobbym wrote:

I am also impressed with how quickly you pick things up.

...with my free hand I was able to pick up the cup of tea that I knocked off the desk just as it hit the floor - all without spilling a drop.

Btw, I don't know how you would have known about my exceptionally-quick manual dexterity.

Last edited by phrontister (2010-02-23 10:14:42)

bobbym · 2010-02-23 13:49:32

The word has gotten around.

Math Is Fun Forum

#26 2010-02-21 08:12:51

Re: I've found this to be INTERESTING..

#27 2010-02-21 09:51:31

Re: I've found this to be INTERESTING..

#28 2010-02-21 09:59:42

Re: I've found this to be INTERESTING..

#29 2010-02-21 10:04:13

Re: I've found this to be INTERESTING..

#30 2010-02-21 22:40:21

Re: I've found this to be INTERESTING..

#31 2010-02-22 01:26:48

Re: I've found this to be INTERESTING..

#32 2010-02-22 04:23:34

Re: I've found this to be INTERESTING..

#33 2010-02-22 04:40:24

Re: I've found this to be INTERESTING..

#34 2010-02-22 05:01:15

Re: I've found this to be INTERESTING..

#35 2010-02-22 19:29:51

Re: I've found this to be INTERESTING..

#36 2010-02-23 09:14:44

Re: I've found this to be INTERESTING..

#37 2010-02-23 09:33:11

Re: I've found this to be INTERESTING..

#38 2010-02-23 13:49:32

Re: I've found this to be INTERESTING..

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