Mirror Odometer: 15951
Read the puzzle
A car odometer reads 15951 km. This is a mirror number: it reads the same forwards and backwards, like 12321. The odometer keeps counting up one kilometre at a time. How many more km until it next shows a mirror number?
How many more km until the next mirror number?
The middle digit is already 9, so it cannot go up. What has to change instead?
110 km
The next mirror number is 16061: 16061 − 15951 = 110.
How to solve it
A five-digit mirror number has the shape a b c b a: the first digit matches the last, and the second matches the fourth. The next one must be the smallest such number above 15951.
Step one: try to keep 1 5 _ 5 1 and raise only the middle digit. The middle is already 9, the largest digit, so nothing of the form 15c51 is bigger. That shape is used up.
Step two: raise the second digit instead, from 5 to 6. The fourth digit must match, so the number becomes 1 6 c 6 1. Choose the smallest middle, 0, giving 16061.
Step three: subtract. 16061 − 15951 = 110 km.
A common wrong answer is 100, from picking 16051. But 16051 reads 15061 backwards, so it is not a mirror number; the second and fourth digits must change together. Another slip is 1010, from 16961, which skips the smaller 16061.
Quick check: 15951 + 110 = 16061, and 16061 reversed is 16061.
