## 14. Math Puzzle $7 / 66$

While the truck driver was checking his odometer during the drive, it showed $15951 \mathrm{~km}$. He noticed that this reading was a symmetrical number, a number that reads the same forwards and backwards.

After two hours of driving, the odometer again displayed a number that reads the same forwards and backwards. At what average speed did the vehicle travel during these two hours?
It is likely that the next symmetrical number is the one obtained by changing the third digit of 15951 to the next higher digit, because changing the second-to-last digit also changes the second digit, and changing the last digit also changes the first digit, meaning the difference would be one or two orders of magnitude higher.

Now, the third digit is a 9. It becomes 0, as it cannot become 10, and at the same time, the second digit must be increased to 6, which also requires increasing the second-to-last digit to 6.

Thus, the next symmetrical number is 16061. The distance covered is $110 \mathrm{~km}$. This results in an average speed of $55 \frac{\mathrm{km}}{\mathrm{h}}$.

It would theoretically be possible for the odometer to show a higher symmetrical number. The next one would be 16161.

In that case, the average speed would have to have been $105 \frac{\mathrm{km}}{\mathrm{h}}$, which is not only unlikely but also not allowed according to the Road Traffic Regulations.