Math Is Fun Forum

atut

Member

Registered: 2008-04-23

Posts: 30

Plz Help

In the below algebra problems, replace the same characters by the same numerals so that the mathematical operations are correct.

ABCB - DEFC = GAFB
:        +       -
DH   x   AB  =  IEI
-------------------------
GGE + DEBB = DHDG

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Plz Help

I'm gonna program this into my computer and I'll post the answer later, so check back in say 3 hours...

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igloo myrtilles fourmis

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Plz Help

I'm not entirely sure, but I don't think there's a solution to this. At least, not one where each letter corresponds to a different number.

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

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Plz Help

I don't know, I haven't given it much thought.
I started to try programming with a C calculator program
I made once with a macro sort-of language in it, but
it is too slow for my 8000 x 9000 x 90 x 90 looping quick way.

If I get the time, I'll try to program it another way...
Sorry I didn't solve it, if it can be done...

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igloo myrtilles fourmis

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Plz Help

Hi atut;

Your problem yields the following equations:

ABCB - DEFC  = GAFB
DH    *    AB  = IEI
GGE  +  DEBB =  DHDG
ABCB /  DH  = GGE         ( ABCB -  DH  = GGE has no solutions )
DEFC + AB = DEBB
GAFB - IEI = DHDG

There is only one solution:
A  =  3
B  =  8
C  =  0
D  =  1
E  =  4
F  =  5
G =  2
H =  7
I  =   6

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,823

Re: Plz Help

That was an interesting one.

I got the same answer as you, Bobby.

I coded these two equations in LB, hoping for fewer solutions than with the other four equations because of the division and multiplication operations:

The first gave

solutions and the second one

.

That provided enough info to find the unique solution with quite a short manual process of eliminations.

Last edited by phrontister (2010-06-22 06:07:27)

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Plz Help

Hi phrontister;

Yes, I noticed that also if you solve them both at the same time it reduces the answer to one! So you really only need the first 2 equations.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,823

Re: Plz Help

Hi Bobby,

I hadn't considered trying for just a computer solution.

Yes...using the first two equations in your list solved the puzzle in one go, as they contain all 9 letters and the solution is unique.

In my program I included a check for the other four equations.

LB's output:

ABCB | DEFC | GAFB
------------------
3808 - 1450 = 2358

DH | AB | IEI
-------------
17 x 38 = 646

A = 3
B = 8
C = 0
D = 1
E = 4
F = 5
G = 2
H = 7
I = 6

END

Last edited by phrontister (2010-06-23 05:33:22)

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Plz Help

Hi phrontister;

I don't usually do any cleaning up of these type of problems. First because it usually loses solutions and second because by the time you clean it up the computer is usually done with the uncleaned program. In this case...

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,823

Re: Plz Help

Just being tidy while watching Isner vs Mahut...40-all in the 5th set!!! Many world records set!

Checking those four equations was pretty straightforward:

if val(G$+G$+E1$) + val(D$+E1$+B1$+B1$) = val(D$+H$+D$+G$) then
    if val(A1$+B1$+C1$+B1$) / val(D$+H$) = val(G$+G$+E1$) then
        if val(D$+E1$+F1$+C1$) + val(A1$+B1$) = val(D$+E1$+B1$+B1$) then
            if val(G$+A1$+F1$+B1$) - val(I1$+E1$+I1$) = val(D$+H$+D$+G$) then

Last edited by phrontister (2010-06-23 06:24:32)

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Plz Help

I take it you are home then and relaxing.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,823

Re: Plz Help

Yes. I enjoy watching the tennis. But it's verrrry late. Bed soon.

I just worked out how to simplify that equation-checking code...by concatenating the string variables. Easy! Hadn't thought of that before. I've changed the code in my previous post.

I guess I think better when I'm dog-tired!

my 10 miles of code (don't laugh!). Anyway, it works...and, I think, covers all bases. Takes 110 seconds. It may look harder than it really is, but basically I just altered another alphametic solution, where most of the thinking was already done.

Last edited by phrontister (2010-06-23 16:44:23)

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Plz Help

It's like 4 AM there isn't it? That is late.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,823

Re: Plz Help

Yes. Still watching Isner vs. Mahut, which is 48 all in the 5th set!!!!!!!! That one set's been going for 5 and a half hours, which is a couple of hours longer than most entire matches!

Their total court time is about 9 hours so far!

Last edited by phrontister (2010-06-23 06:50:33)

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Plz Help

Hi phrontister;

Watched it to 59 - 59.  Hard to believe that two guys rated 140 and 19th can play that well.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,823

Re: Plz Help

Hard to believe that two guys rated 140 and 19th can play that well.

The depth of men's tennis is very strong.

What is particularly good about Mahut, the so-called weaker of the two, is that, unlike Isner, he had to play in the qualifying tournament...AND one of his matches went to 24-22 in the third (last) set. As someone commented, "He's hard to put away"!!

Interesting to do the sums on their aces:

Isner 98 + Mahut 95 = 193

That is equivalent to a 6-4, 6-4, 4-6, 4-6, 6-3 match in which all strokes except 3 are aces!

Isner is renowned for his serving ability, while Mahut is not; yet their stats are nearly equal. 'Early' in the match there was a large margin between their ace count. That shows the different impact this draining match had on them as the game wore on.

Most of the records set in that amazing match will never be broken.

Last edited by phrontister (2010-06-24 00:51:43)

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Plz Help

Yes, that is interesting. spreading 193 aces over a five set match is going to be hard. They are serving well.

Do you know there is another possible set of scores for a five game set other than 6-4, 6-4, 4-6, 4-6, 6-3, that is also 193 out of 196?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,823

Re: Plz Help

4-6, 6-4, 4-6, 6-4, 6-3.

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Plz Help

Hi phrontister;

Yes, that is true, but I meant different set scores other than (4-6, 6-4, 4-6, 6-4, 6-3)

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,823

Re: Plz Help

Not quite the answer to your question, but:

7-6 (7-2 in the tiebreak), 6-4, 4-6, 1-6, 1-6 = 193.

Last edited by phrontister (2010-06-24 01:14:02)

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Plz Help

Yes, there is one more I know of, it has no tiebreakers. Not at as good as 193 though!

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,823

Re: Plz Help

7-5, 6-4, 4-6, 4-6, 6-1

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Plz Help

I didn't get that one, good one! There is still another with no score bigger than 6.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,823

Re: Plz Help

6-4, 6-4, 4-6, 4-6, 5-4 (retired)

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Plz Help

That's good! Sorry, I had an error. I think you got em all. At least I don't think there are anymore with no score bigger than 6.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.