### Legs Eleven

Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?

### How Many Miles to Go?

How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?

### Farey Sequences

There are lots of ideas to explore in these sequences of ordered fractions.

# Tick Tock

##### Age 11 to 14 ShortChallenge Level

Tick's watch is 2 minutes slow per hour, Tock's is 1 minute fast per hour, so Tock's watch is faster than Tick's watch by 3 minutes per hour.

Correct time Tick's Watch Tock's Watch Difference
12:00 12:00 12:00 -
13:00 12:58 13:01 3 minutes
14:00 13:56 14:02 6 minutes

They get 3 minutes further apart after each 1 hour.

They will be 60 minutes further apart after 20 hours.

20 hours after midday on Sunday is 8 am on Monday.

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.