Mileage

[Ian Volante]

While driving northwards last night, I noticed my milometer click over to a palindromic total. 11 miles later, it was again palindromic. After driving a further 17 miles, it won't now be palindromic again for 9,993 miles. How many miles has my car covered?

[Gavin Chipper]

If it had travelled 199991 miles, then after another 11 it would be on 200002 (also palindromic). Then after another 17 miles, it would be on 200019, but you didn't specify that this number had to be palindromic. Another 9993 miles later and it will be 210012. So the answer is 200019.

[Graeme Cole]

After driving a further 17 miles, it won't now be palindromic again for 9,993 miles.

Don't you mean 1,083?

[Graeme Cole]

If it had travelled 199991 miles, then after another 11 it would be on 200002 (also palindromic). Then after another 17 miles, it would be on 200019, but you didn't specify that this number had to be palindromic. Another 9993 miles later and it will be 210012. So the answer is 200019.

I had 100018, but I was counting 099990 as palindromic.

[Ian Volante]

Well done Mr Chipper. You are correct. Want to buy a car?

Graeme, counting leading zeroes would just have been perverse

[Gavin Chipper]

Well done Mr Chipper. You are correct. Want to buy a car?

Graeme, counting leading zeroes would just have been perverse

Depends. How many miles has it done?

Counting leading zeroes isn't that perverse given that milometers show them - particularly old ones!