I know that

| 191*A = 70*B + 898*C

| 70*B = 191*A - 898*C

| 898*C = 191*A - 70*B

I can say for sure that C<A

But can I say B>A without guessing ?

(A,B,C are natural numbers 0-9)

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- Oct 23rd 2011, 01:00 AMPhaireroIs B bigger than A?
I know that

| 191*A = 70*B + 898*C

| 70*B = 191*A - 898*C

| 898*C = 191*A - 70*B

I can say for sure that C<A

But can I say B>A without guessing ?

(A,B,C are natural numbers 0-9) - Oct 23rd 2011, 01:53 AMsbhatnagarRe: Is B bigger than A?
- Oct 23rd 2011, 01:55 AMPhaireroRe: Is B bigger than A?
Well, some include 0 too.

What I meant was they are ... numbers from 0-9

as in (0,1,2,3,4,5,6,7,8,9)

*(***Edit (added) :**NOT 1,3 or pi or 3,89 or something else like that)

What were they called... oh, one-digit numbers!

Sorry my bad.

Can you help me now? - Oct 23rd 2011, 02:44 AMsbhatnagarRe: Is B bigger than A?
Our equation is

**Part 1)**

The equation can be rearranged to form

We know that (C is positive, so a positive no times a negative no is negative), so LHS is negative & and are positive so this leads us to the fact that .

**Part 2)**

The equation can be rearranged to form

Again here, - Oct 23rd 2011, 02:48 AMPhaireroRe: Is B bigger than A?
Yes, I apologize If I can't read it out, but where does it say then, that B > A ?

Can I say it?

I already know the answer I just need to know if I can say that B is bigger than A

If I can't say it my whole solution might just fall apart. - Oct 23rd 2011, 03:11 AMsbhatnagarRe: Is B bigger than A?
You may or may not say that because we found in part 1 that . This does not tell us whether or .

In part 2 we found that but here so we can easily say that . - Oct 23rd 2011, 03:24 AMPhaireroRe: Is B bigger than A?
That is sad...

Then how am I supposed to figure this out

1998*ABC=CBA*8991

ABC = 3 digit number

CBA = same 3 digit number written backwards

A,B,C are one digit numbers.

What I did until that.

1998 * ABC = CBA * 8991

1998 * (100A + 10B + 1C) = (100C + 10B + 1A) * 8991

199800A + 19980B + 1998C = 899100C + 89910B + 8991A

199800A - 8991A = 89910B - 19980B + 899100C - 1998C

190809A = 69930B + 897102C |divided by 9

21201A = 7770B + 99678C |divided by 3

7067A = 2590B + 33226C |divided by 37

191A = 70B + 898C

191 is a prime number, so I can't divide any further. - Oct 23rd 2011, 05:23 AMSorobanRe: Is B bigger than A?
Hello, Phairero!

Quote:

Solve the alphametic: .

= 3-digit number

= same 3 digit number written backwards

are digits.

We have: . . .

Divide by 999: w

. . . .

. . . . . .

. n . . . . . . . . . . . . .[1]

. n . . . . . . . . . . . .

. . . . . . . . . . . . . . .

Multiply by 11:. . . .

. w . . . . . . . . . . . . . .

Since and are digits: .

Substitute into [1]: .

. . Hence: .

Therefore: .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

**Check**:. .

- Oct 23rd 2011, 06:24 AMPhaireroRe: Is B bigger than A?
I did some research, and understood most of it, except how you got from

http://latex.codecogs.com/png.latex?...mod%2070%29%7D

to

http://latex.codecogs.com/png.latex?...mod%2070%29%7D

EDIT :

And from this

http://latex.codecogs.com/png.latex?...mod%2070%29%7D

to

http://latex.codecogs.com/png.latex?...mod%2070%29%7D

or can I just write them there and every teacher/tutor/professor/smarter-person-than-me would understand me?