Clock and Calendar Numbers

Clock Patterns

Digital clocks show patterns like:

• Repeated Digits: $11:11, 22:22$ (on 24h clock), $4:44$.
• Palindromic Times: $10:01, 12:21, 05:50$.

Problem: Next Palindrome

If the time is 10:01, when is the next palindromic time?

1. The hours are 10. The only palindrome with 10 is 10:01.
2. Next hour is 11. Palindromes: $11:11$.
3. Difference: from 10:01 to 11:11 is 1 hour 10 minutes (70 minutes).

Calendar Patterns

Dates can also be palindromes (e.g., 11/02/2011 reads the same forwards and backwards if we ignore slashes).

Calendar Repetition: Did you know calendars repeat?

• A standard year calendar repeats every 11 years (usually).
• The entire cycle of dates and days repeats every 28 years (guaranteed).