When I bought my first bike , I had to get a license plate. The license number which I got consisted of 5 different digits and by mistake when I fixed it upside down it could still be read, but the value decreased by 78633.
What was my actual license number?
Note: The numbers for number plate are of the style : I , .
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The numbers : I , 6 , 8 , 9 , 0 are the only five numbers that can be read upside down as well.
Let the original number be A B C D E and the the upside down number be F G H I J
A B C D E − F G H I J = 7 8 6 3 3
Clearly A B C D E > 78633, so A must be 8 or 9. We consider the two possibilities separately:
A = 9 : Then 9 B C D E = 78633 + F G H I 6 , so E = 9 . This implies F = 6 , which is impossible, as 78633 + F G H I 6 would be a six-digit number.
A = 8 : Then 8 B C D E = 78633 + F G H I 8 , so E = 1 .
Now we know that the answer must have A = 8 and E = 1 , i.e.,
8 B C D 1 − 1 G H I 8 = 7 8 6 3 3 .
Note that 8 B C D 1 = 7 8 6 3 3 + 1 G H I 8 > 7 8 6 3 3 + 1 0 0 0 0 = 8 8 6 3 3 , so B must be 8 or 9.
Since all the numbers are distinct ,thus B = 9 : Then 8 9 C D 1 = 7 8 6 3 3 + 1 G H 6 8 , so D = 0
Thus C = 6
The answer is 8 9 6 0 1