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 Four Digit Number II (Posted on 2003-07-06)
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: (Hide) 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.

Comments: ( You must be logged in to post comments.)
 Subject Author Date Puzzle Resolution K Sengupta 2007-07-11 09:20:43 Visual approach Steve Herman 2004-10-23 14:04:19 solution ben young 2003-07-14 03:03:59 re: Non-algorithmic solution Gamer 2003-07-12 08:28:02 answer kevin 2003-07-08 10:06:03 re: Non-algorithmic solution Jim C 2003-07-07 08:22:05 Thank God I have all of MY digits! Jim C 2003-07-07 08:14:27 Solution (Algebraic) ryan smith 2003-07-06 20:04:10 Non-algorithmic solution TomM 2003-07-06 13:02:15 re(2): Solution Charlie 2003-07-06 06:09:26 re: Solution Charlie 2003-07-06 06:07:14 Solution Lewis 2003-07-06 04:45:24
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