Math Is Fun Forum / Add ABC + DEF = GHI. Also, ADG + BEH = CFI

Michaelangelo · 2007-09-12 22:39:31

ABC + DEF = GHI

(and)

ADG + BEH = CFI

where each letter represents a number 1-9.

Can you figure it out?

landof+ · 2007-09-12 23:43:07

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

Devantè · 2007-09-13 16:08:00

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 ... ?

landof+ · 2007-09-13 23:14:04

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

Devantè · 2007-09-14 03:40:24

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

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

landof+ · 2007-09-15 22:58:55

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?

Code:

 ABC
+DEF
----
 GHI

and this

Code:

 ADG
+BEH
----
 CFI

That'll make it easier...

Last edited by landof+ (2007-09-15 22:59:14)

Devantè · 2007-09-16 01:13:49

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.

mathsyperson · 2007-09-16 01:28:05

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

Devantè · 2007-09-16 02:38:13

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.

mathsyperson · 2007-09-16 03:00:46

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.

bugmenot · 2010-04-04 04:32:17

Sorry, but... how about:
ABDBC=DEF/GHI ? //the same rules//

I've been crushing my head to solve this for a few days...
[EDIT:]
I meant "ABDBC=DEF*GHI", as posted below...

Last edited by bugmenot (2010-04-04 07:09:03)

bobbym · 2010-04-04 06:13:03

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?

bugmenot · 2010-04-04 07:05:38

Sry, I meant ABDBC=DEF*GHI
Sorry

bobbym · 2010-04-04 07:16:21

Hi;

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

bugmenot · 2010-04-04 07:21:47

How do You know it so quickly?

bobbym · 2010-04-04 07:25:39

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.

bugmenot · 2010-04-04 08:23:09

Well, thank You.
Nice dreams! q

bobbym · 2010-04-04 08:41:21

Hi bugmenot;

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

Kalipso · 2010-08-16 09:30:58

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

bobbym · 2010-08-16 09:42:23

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.

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#1 2007-09-12 22:39:31

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

#2 2007-09-12 23:43:07

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

#3 2007-09-13 16:08:00

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

#4 2007-09-13 23:14:04

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

#5 2007-09-14 03:40:24

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

landof+ wrote:

#6 2007-09-15 22:58:55

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

Michaelangelo wrote:

Code:

Code:

#7 2007-09-16 01:13:49

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

#8 2007-09-16 01:28:05

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

#9 2007-09-16 02:38:13

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

#10 2007-09-16 03:00:46

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

#11 2010-04-04 04:32:17

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

#12 2010-04-04 06:13:03

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

#13 2010-04-04 07:05:38

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

#14 2010-04-04 07:16:21

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

#15 2010-04-04 07:21:47

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

#16 2010-04-04 07:25:39

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

#17 2010-04-04 08:23:09

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

#18 2010-04-04 08:41:21

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

#19 2010-08-16 09:30:58

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

#20 2010-08-16 09:42:23

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

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