### Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

### Calendar Capers

Choose any three by three square of dates on a calendar page...

### Days and Dates

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

# Reading from Behind

##### Stage: 3 Short Challenge Level:

Reading the digits from behind is the same as reflecting them in a vertical line of symmetry. This means $0$ and $8$ are read as themselves, and $2$ and $5$ are swapped. Note that the digits are read in the opposite order

Since the time is before $10:00$, the first hour digit must be a $0$. When read from behind, this means the last digit must also be a $0$. Since the time is between $3:00$ and $10:00$ and the second hour digit must be one that reads backwards as another digit, it must be either $5$ or $8$.

Since $08:80$ is not a valid time, the time must be $05:20$.

This problem is taken from the UKMT Mathematical Challenges.