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Four Digit Number II (Posted on 2003-07-06) |
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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.
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Submitted by Gamer
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Rating: 3.0000 (4 votes)
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Solution:
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(Hide)
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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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