Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#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?

Offline

#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...

Offline

#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 ... ?

Offline

#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...

Offline

#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?

Offline

#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...

Offline

#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.

Offline

#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.

Offline

#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.

Offline

#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.

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,799

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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,799

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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,799

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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,799

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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#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?

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,799

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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

Board footer

Powered by FluxBB