Math Is Fun Forum

actour50

Member

Registered: 2008-02-01

Posts: 0

Find the numbers! (Algerbra problem) :)

Donald+ Gerald= Robert
t= 0
Find the numbers!

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Find the numbers! (Algerbra problem) :)

So, d must be 5 ...

---

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

Zach

Member

Registered: 2005-03-23

Posts: 2,075

Re: Find the numbers! (Algerbra problem) :)

Donald + Gerald = 0.

---

Boy let me tell you what:
I bet you didn't know it, but I'm a fiddle player too.
And if you'd care to take a dare, I'll make a bet with you.

pi man

Member

Registered: 2006-07-06

Posts: 251

Re: Find the numbers! (Algerbra problem) :)

DONALD
GERALD
=====
ROBERT

T=0, Therefore D must be 5

5ONAL5
GERAL5
=====
ROBER0

From O + E = O, E must be 0 or 9 (carry one).   Can't be 0, must be 9

5ONAL5
G9RAL5
=====
ROB9R0

From A+A=9, A must be either 4 or 9 with a "carry one" from L+L.  Can't be 9.

5ON4L5
G9R4L5
=====
ROB9R0

So far we have:
T = 0
D = 5
E = 9
A = 4

We still have 1, 2, 3, 6, 7, 8.   Using L + L = R (plus a "carry one") and R + G = 5 (also a carry one) we have the following possibilities

L =  1   2   3   6   7  or 8
R =  3   5   7   3   5  or 7
G =  1  -1 -3   1  -1 or -3

So G=1, R=3 and L=6

5ON465
193465
=====
3OB930

That leaves 2, 7 and 8 for B, N and O.   We know N+3=B but none of the number combinations we have left will work.   So either:  I did something wrong, I assumed something I shouldn't have (there is a 1-to-1 mapping between letters and numbers), the problem as stated doesn't have a valid answer.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Find the numbers! (Algerbra problem) :)

5ON4L5
G9R4L5
=====
ROB9R0

So far we have:
T = 0
D = 5
E = 9
A = 4

We still have 1, 2, 3, 6, 7, 8.

I think you're alright up to here, but then you make some mistakes in your column interpretations.

I think we have:

L+L-9 = R (because 1 is carried to this column and 10 is carried from it)
N+R-10 = B (because 10 is carried from this column)
6+G = R (because 1 is carried to this column)

The first equation means that L is 6, 7 or 8.
That means that R is 3, 5 or 7 respectively.
7 is the only one of those that works with the third equation, so now we have:

5ON485
197485
=====
7OB970

We're now left with 2, 3 and 6.
The second equation has now become N-3 = B, and the only way to make that work is with 6 and 3.
That leaves O stuck as 2.

Final answer:

526485
197485
=====
723970

0 T
1 G
2 O
3 B
4 A
5 D
6 N
7 R
8 L
9 E

---

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

pi man

Member

Registered: 2006-07-06

Posts: 251

Re: Find the numbers! (Algerbra problem) :)

Yep, I messed up on calculating G.   But I was still correct because I said one of the possibilities was that I did something wrong!   CYA!

Last edited by pi man (2008-02-04 17:24:37)