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ABCDC - BEAAC = BADADDate: 03/25/2002 at 20:09:00 From: Arthur Subject: Wierd math problem ABCDC - BEAAC = BADAD If D=0 the point of this problem is to find out what all the letters stand for knowing that d is equal to zero and the problem has to equel BADAD. Thanks, Arthur R.
Date: 03/26/2002 at 08:21:02
From: Doctor Ian
Subject: Re: Wierd math problem
Hi Arthur,
Here is the original problem:
ABCDC
- BEACC
-------
BADAD
We're told that D is zero - although that's not much of a hint. (Do
you see why it can't really be anything else?)
ABC0C
- BEACC
-------
BA0A0
If we assume that each letter has to stand for a different digit, then
we can look at the tens place,
ABC0C
- BEACC
-------
BA0A0
^
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and see that we're going to have to carry a 1 from the hundreds place,
which means that 9-C = A. If nothing else, this means that if we ever
figure out what C is, we'll know what A has to be; or if we ever
figure out what A is, we'll know what C has to be. So let's include
that in what we know:
ABC0C 9 - C = A
- BEACC
-------
BA0A0
Now, when we carried that 1, we were left with C-1 on top in the
hundreds column. If there are no other carries, then it must be true
that
(C-1) - A = 0
If there is a carry to that column, then it must be true that
C - A = 0
But this would mean that A and C are equal; and we're assuming that
each letter has to be a different digit. So we can rule this out.
Therefore, we know that
(C-1) - A = 0
C - 1 = A
So let's add that to what we know:
ABC0C 9 - C = A
- BEACC C - 1 = A
-------
BA0A0
Now, this is interesting, because we have two equations with two
variables; and that means there is only one pair of values that can
make both equations true.
9 - C = A
C - 1 = A
In fact, the two things on the left are both equal to the same thing,
so they must be equal to each other:
9 - C = C - 1
Can you solve this to get C? That will tell you the value of A as
well. And that should get you most of the way towards a solution.
Can you take it from here?
- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
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