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Date: 01/25/2002 at 10:34:21
From: Ting Zi

I am stuck on this maths problem. Here is the question:

You can only use the numbers 0 to 9 for each letter once.

G*B=HA
D*E=E
I*C=C
H*A=DE
F*J=GJ

*=TIMES

Can you please explain how to do this problem?
Ting Zi
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```
Date: 01/25/2002 at 17:01:13
From: Doctor Peterson

Hi, Ting.

Could you show me what ideas you had? You may have been close to an
answer and only made some little mistakes, or you may not have been
trying the right approach. This takes a little thinking, and I want to
give you only the hints you need so you can have the experience of

The first things I notice are

D*E=E
I*C=C

There are only two ways that a number can be multiplied by another
number and be left unchanged: either the multiplier is 1, or the
number that stays the same is 0. So there are two possibilities:

D=1, C=0, so 1*E=E and I*0=0

I=1, E=0, so D*0=0 and 1*C=C

You can try each of these possibilities and see what happens as you
continue thinking. When you determine whether there is any solution
making one assumption, switch to the other assumption and try again.

You can also look at

F*J=GJ

and make a list of all possible products of this form. You can ignore
any for which any of the digits are 0 or 1, or where two other than
the J's are the same (such as 6*2=12). This will leave only four
possibilities, I believe, which determine the choices for G.

Then look at

G*B=HA
H*A=DE

You will have chosen a value for D or E, so you can find all
possibilities for H*A, and then see which can be factored to give G*B.

If you need more than these hints, write back and show your thinking
as far as you get, so I can help where you really need help.

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
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