It can be read upside down as well!

Logic Level 4

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 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 0 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 0 .


The answer is 89601.

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1 solution

Ratul Pan
Mar 1, 2017

The numbers : I , 6 , 8 , 9 , 0 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 \overline{ABCDE} and the the upside down number be F G H I J \overline {FGHIJ}

A B C D E F G H I J = 78633 \overline{ABCDE} - \overline {FGHIJ} = 78633

Clearly A B C D E \overline{ABCDE} > 78633, so A A must be 8 or 9. We consider the two possibilities separately:

A = 9 A=9 : Then 9 B C D E \overline{9BCDE} = 78633 + F G H I 6 \overline {FGHI6} , so E = 9 E=9 . This implies F = 6 F=6 , which is impossible, as 78633 + F G H I 6 \overline {FGHI6} would be a six-digit number.

A = 8 A=8 : Then 8 B C D E \overline{8BCDE} = 78633 + F G H I 8 \overline {FGHI8} , so E = 1 E=1 .

Now we know that the answer must have A = 8 A=8 and E = 1 E=1 , i.e.,
8 B C D 1 1 G H I 8 = 78633 \overline{8BCD1} - \overline{1GHI8} = 78633 .

Note that 8 B C D 1 = 78633 + 1 G H I 8 > 78633 + 10000 = 88633 \overline{8BCD1} = 78633 + \overline{1GHI8} > 78633 + 10000 = 88633 , so B B must be 8 or 9.

Since all the numbers are distinct ,thus B = 9 B=9 : Then 89 C D 1 = 78633 + 1 G H 68 \overline{89CD1} = 78633 + \overline{1GH68} , so D = 0 D=0

Thus C = 6 C = 6

The answer is 89601 \boxed {89601}

The number must contain 0 , 1 , 6 , 9 , 8 0,1,6,9,8 because these are the only numbers which can be read by upside down properly

Kushal Bose - 4 years, 3 months ago

Cool problem ! It was really fun to solve.

saharsh rathi - 4 years, 2 months ago

what about 89201?

Hasmik Garyaka - 2 years, 4 months ago

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2 cannot be read upside down.

Ratul Pan - 2 years, 2 months ago

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