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Four Digit Number II (Posted on 20030706) 

Pick a four digit number, all digits different, such that when you add its reverse and divide it by 10, you get the number you started with.
For example: 1749+9471=11220, 11220/10 = 1122. Since 1749 is not equal to 1122, this is not the right number.

Submitted by Gamer

Rating: 3.0000 (4 votes)


Solution:

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So far, the equation is:
_abcd
+dcba

abcd0
It must end in 0 in order to come out with no decimal. a must equal 0 or 1. If a = 0, d = 0, and d = a, which is not allowed. So a must equal 1.
_1bcd
+dcb1

1bcd0
Since d+1=0, d must equal 9.
_1bc9
+9cb1

1bc90
Now, b must equal 1 or 0. If b = 1, then a = b, which is not allowed. So b = 0.
_10c9
+9c01

10c90
Noting that 9+1 = 0 carries a 1, 1+c+0 = 9, c = 8, so:
_1089
+9801

10890
This shows that 1089 is the only possible solution. 
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