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

ABC + DEF = GHI

(and)

ADG + BEH = CFI

where each letter represents a number 1-9.

Can you figure it out?

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

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

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

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

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

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

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

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

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

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

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

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.

Why did the vector cross the road?

It wanted to be normal.

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

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

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

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

Hi bugmenot;

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

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

Combinatorics is Algebra and Algebra is Combinatorics.

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

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

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.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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