Question 803357
If You Multiply 4321 By A Certain 4-digit Number, The 8-digit Answer You Get Ends In Its Reverse

<pre>
In the multiplication below, the "0"'s
are zeros, and the letter "O" is not
used, and the small a,b,c are not the
same as the capital letters A,B,C.

      4321
      <u>ABCD</u>
     EFGHI
    JKLMN0
   PQRST00
  <u>UBWXY000</u>
  Zabc1234

We see that I=4, thus D=4 and
EFGHI = 17284

 
      4321
      <u>ABC4</u>
     17284
    JKLMN0
   PQRST00
  <u>UBWXY000</u>
  Zabc1234

We see that N=C and N=5 so that
8+5=13, so we put 5's for C and N,
and remember that 1 is carried to
the third column in the addition: 

      4321
      <u>AB54</u>
     17284
    JKLM50
   PQRST00
  <u>UBWXY000</u>
  Zabc1234

Now we see that JKLM = 2160
    
      4321
      <u>AB54</u>
     17284
    216050
   PQRST00
  <u>UBWXY000</u>
  Zabc1234

Now since there was a 1 carried
to the third column, T=9, and that
makes B=9 as well, and we remember
that a 1 is carried to the 4th
column in the addition:

      4321
      <u>A954</u>
     17284
    216050
   PQRS900
  <u>UBWXY000</u>
  Zabc1234

Now we see that PQRS = 3888

      4321
      <u>A954</u>
     17284
    216050
   3888900
  <u>UBWXY000</u>
  Zabc1234

If we remember that ther was a 1
carried to the 4th column then when
we add 1+7+6+8+Y to get a number
ending in 1, Y must be 9 so that
1+7+6+8+9=31, with 3 to carry to the
5th column.  And so A=9

      4321
      <u>9954</u>
     17284
    216050
   3888900
  <u>UBWX9000</u>
  Zabc1234

Now we have the answer, 9954, but
here are the rest of the digits:

      4321
      <u>9954</u>
     17284
    216050
   3888900
  <u>38889900</u>
  43011234

Edwin</pre>