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#1 2007-09-12 00:39:31

Michaelangelo
Member
Registered: 2007-09-12
Posts: 1

Add ABC + DEF = GHI. Also, ADG + BEH = CFI

ABC + DEF = GHI

(and)

ADG + BEH = CFI

where each letter represents a number 1-9.

Can you figure it out?

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#2 2007-09-12 01:43:07

landof+
Member
Registered: 2007-03-24
Posts: 131

Re: Add ABC + DEF = GHI. Also, ADG + BEH = CFI

They are related, and A,B,C,D,E,F,G,H,I are all the same digits in both sums right? neutral


I shall be on leave until I say so...

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#3 2007-09-12 18:08:00

Devantè
Real Member
Registered: 2006-07-14
Posts: 6,400

Re: Add ABC + DEF = GHI. Also, ADG + BEH = CFI

Either C + F = I OR C + F - 10 = I
Either G + H = I OR G + H - 10 - I
If G + H = I, F is an even number and D is not equal to five.
A + D < 10
A + B < 10

Simplified:

8D + E - 9B = (G + H - C - F) / 10

I did some research on the internet, and some person wrote a C++ program to test every possible conbination. Turns out there was no solution.

So, the answer is 8D + E - 9B = (G + H - C - F) / 10 ... ?

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#4 2007-09-13 01:14:04

landof+
Member
Registered: 2007-03-24
Posts: 131

Re: Add ABC + DEF = GHI. Also, ADG + BEH = CFI

Put it into working form, Devantè, sometimes automatic applets just don't work.


I shall be on leave until I say so...

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#5 2007-09-13 05:40:24

Devantè
Real Member
Registered: 2006-07-14
Posts: 6,400

Re: Add ABC + DEF = GHI. Also, ADG + BEH = CFI

landof+ wrote:

Put it into working form, Devantè, sometimes automatic applets just don't work.

Erm, I don't understand ... 'working form'? Of what?

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#6 2007-09-15 00:58:55

landof+
Member
Registered: 2007-03-24
Posts: 131

Re: Add ABC + DEF = GHI. Also, ADG + BEH = CFI

Michaelangelo wrote:

ABC + DEF = GHI

(and)

ADG + BEH = CFI

where each letter represents a number 1-9.

Can you figure it out?

hmmm....
How about this?

 ABC
+DEF
----
 GHI

and this

 ADG
+BEH
----
 CFI

That'll make it easier...:)

Last edited by landof+ (2007-09-15 00:59:14)


I shall be on leave until I say so...

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#7 2007-09-15 03:13:49

Devantè
Real Member
Registered: 2006-07-14
Posts: 6,400

Re: Add ABC + DEF = GHI. Also, ADG + BEH = CFI

ABCDEFGHI    ABC + DEF = GHI    ADG + BEH = CFI
023594617    023 + 594 = 617    056 + 291 = 347
023695718    023 + 695 = 718    067 + 291 = 358
045876921    045 + 876 = 921    089 + 472 = 561
056291347    056 + 291 = 347    023 + 594 = 617
067291358    067 + 291 = 358    023 + 695 = 718
067854921    067 + 854 = 921    089 + 652 = 741
089472561    089 + 472 = 561    045 + 876 = 921
089652741    089 + 652 = 741    067 + 854 = 921

ABCDEFGHI    ABC + DEF = GHI    ADG + BEH = CFI
326584910    326 + 584 = 910    359 + 281 = 640
348562910    348 + 562 = 910    359 + 461 = 820
359281640    359 + 281 = 640    326 + 584 = 910
359461820    359 + 461 = 820    348 + 562 = 910

ABCDEFGHI    ABC + DEF = GHI    ADG + BEH = CFI
146583729    146 + 583 = 729    157 + 482 = 639
157482639    157 + 482 = 639    146 + 583 = 729
718236954    718 + 236 = 954    729 + 135 = 864
729135864    729 + 135 = 864    718 + 236 = 954

W00T for programming.

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#8 2007-09-15 03:28:05

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: Add ABC + DEF = GHI. Also, ADG + BEH = CFI

Ooh, nice. Depending on the rules, that first set might not count, but we've still got 8 good answers there.


Why did the vector cross the road?
It wanted to be normal.

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#9 2007-09-15 04:38:13

Devantè
Real Member
Registered: 2006-07-14
Posts: 6,400

Re: Add ABC + DEF = GHI. Also, ADG + BEH = CFI

where each letter represents a number 1-9.

This part of the puzzle is the tricky bit; If that is indeed one of the actual rules to this puzzle, then yes, I only have 8 answers.

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#10 2007-09-15 05:00:46

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: Add ABC + DEF = GHI. Also, ADG + BEH = CFI

Oh, I didn't see that, I was just assuming that the first digit of everything couldn't be 0.
In that case, there are only 4 good answers. Still 400% of what we need though. smile


Why did the vector cross the road?
It wanted to be normal.

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#11 2010-04-03 08:13:03

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,228

Re: Add ABC + DEF = GHI. Also, ADG + BEH = CFI

Hi bugmenot;

If this is what you mean:

There is no solution to that one. ABDBC cannot be an integer. Does the problem have a decimal point that you are forgetting about?


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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#12 2010-04-03 09:16:21

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,228

Re: Add ABC + DEF = GHI. Also, ADG + BEH = CFI

Hi;

No problem. Unfortunately that one doesn't have a solution either. Not unless you have some zeros for letters.


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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#13 2010-04-03 09:25:39

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,228

Re: Add ABC + DEF = GHI. Also, ADG + BEH = CFI

Hi;

I have written a program to do these for me.

You have to be able to recognize a computer problem from a math problem. If you have time please read this:

http://www.artofproblemsolving.com/Foru … p?t=334017

I am of the same opinion today, as then.


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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#14 2010-04-03 10:41:21

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,228

Re: Add ABC + DEF = GHI. Also, ADG + BEH = CFI

Hi bugmenot;

Thanks! Glad to help, and welcome to the forum.

1.gif


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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#15 2010-08-15 11:30:58

Kalipso
Member
Registered: 2010-08-15
Posts: 1

Re: Add ABC + DEF = GHI. Also, ADG + BEH = CFI

Did you ever get a clear answer for this one?  Not just the answer itself but what steps you took to get the answer?

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#16 2010-08-15 11:42:23

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,228

Re: Add ABC + DEF = GHI. Also, ADG + BEH = CFI

Hi Kalipso;

Welcome to the forum! Sometimes you can reason about these but most of the time post #16 holds.

Most of the time there is a big overlap between what is a math problem and what is a programming problem. In some cases there is no overlap or little. I believe these alphametic problems when large are of that type.


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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