Mirror Odometer: 29992
Read the puzzle
A car odometer reads 29992 km, a mirror number that reads the same forwards and backwards, like 12321. The odometer counts 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 9s roll over soon.
11 km
The next mirror number is 30003, just 11 km on.
How to solve it
A five-digit mirror number has the shape a b c b a. Look for the smallest one above 29992 by changing digits from the middle outward.
Step one: the middle digit is 9, so 2 9 c 9 2 cannot get any bigger.
Step two: the second and fourth digits are also 9, so 2 b c b 2 cannot get bigger either. Every mirror number starting and ending in 2 is now used up.
Step three: move to a first digit of 3. The last digit must also be 3, and the smallest choice for the rest is 0s: 30003.
Step four: subtract. 30003 − 29992 = 11 km.
The common wrong answer is a large jump such as 10001 km, from guessing that the next mirror number is 39993. Many people assume mirror numbers are always far apart, but when the 9s roll over the odometer passes a new one quickly.
Quick check: count up from 29992: 29993 ... 29999, then 30000 ... 30003. That is 7 + 4 = 11 steps, and 30003 reads the same both ways.
