A palindromic number is a number whose digits read the same left to right as right to left. For example, 383, 12,321, and 9,876,789 are palindromic. The odometer of the family car read 15,951 when the driver noticed that the number was palindromic. "Curious," said the driver to herself. "It will be a long time before that happens again." But 2 hours later, the odometer showed a new palindromic number. Assuming it was the next possible one, how fast was the car driving in those 2 hours?
try 110 miles :) That would be 55 mph
The ones can not change, but the 9 can become 10
To find the speed at which the car was driving in those 2 hours, we need to calculate the difference between the initial palindromic number (15,951) and the next palindromic number that appeared on the odometer.
The next palindromic number after 15,951 is 16,061.
To calculate the difference, we subtract the initial palindromic number from the next palindromic number:
16,061 - 15,951 = 110
Therefore, the car was driving at a speed of 110 miles per hour in those 2 hours.
To determine the speed of the car in those 2 hours, we need to find the difference between the two palindromic numbers on the odometer.
The current palindromic number is 15,951, and the next possible palindromic number occurs 2 hours later. Let's figure out what that number is.
Since it is the next possible number, we need to iterate through the numbers starting from 15,952 until we find the next palindromic number. Let's write a program that checks for palindromic numbers:
```python
def is_palindrome(n):
return str(n) == str(n)[::-1]
current_number = 15951
next_number = current_number + 1
while not is_palindrome(next_number):
next_number += 1
print(next_number)
```
Running this program will give us the next palindromic number, which is 16,061.
Now, we can calculate the speed of the car by dividing the distance traveled (the difference between the two palindromic numbers) by the time taken (2 hours):
```python
distance_traveled = next_number - current_number
time_taken = 2 # hours
speed = distance_traveled / time_taken
print("The car was driving at a speed of", speed, "units per hour.")
```
Solving this will give us the answer to how fast the car was driving in those 2 hours.