When I acquired my race car, the first thing I had to do was to get a license plate. The plate I got had a peculiar number on it.
It consisted of 5 different numbers and by mistake when I fixed it upside down, the number could still be read, but the value had increased by 78633.
What was my actual license plate number?
details and assumptions
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Let the original license plate number be a b c d e and the reversed one A B C D E . We know that the numbers readable in reverse are 0 , 1 , 6 , 8 , 9 . We are given that A B C D E − e d c b a = 7 8 6 3 3 or:
− A e 7 B d 8 C c 6 D b 3 E a 3
Let's look first pair of digits A and e . For the difference to be 7 , there are only two cases, ( A , e ) = ( 9 , 1 ) or ( 8 , 1 ) . If ( A , e ) = ( 9 , 1 ) , then the last pair of digits are ( 1 , 6 ) and . . . . 1 − . . . . 6 = . . . . 3 , therefore, ( A , e ) = ( 9 , 1 ) and ( A , e ) = ( 8 , 1 ) . And we note that . . . . 1 − . . . . 8 = . . . . 3 .
Similarly, for .(B...-.d...=.8...), ( B , d ) = ( 8 , 0 ) because ( . . . D . − . . . b . = . . . 1 . instead of . . . 3 . .. Therefore, ( B , d ) = ( 9 , 0 ) and ( D , b ) = ( 0 , 6 ) , and we note that . . . 0 . − . . . 6 . = . . . 3 . .
Now, the remaining ( C , c ) . ( C , c ) = ( 0 , 0 ) = ( 1 , 1 ) = ( 8 , 8 ) , else . . C . . − . . c . . = . . 9 . . instead of . . 6 . . . ( C , c ) = ( 6 , 9 ) fits perfectly.
Therefore, the answer is 8 9 6 0 1 − 1 0 9 6 8 = 7 8 6 3 3 , and the original plate number is 1 0 9 6 8 .