### Counting Factors

Is there an efficient way to work out how many factors a large number has?

### Repeaters

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

### Helen's Conjecture

Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?

# Leap Monday

##### Age 11 to 14 Short Challenge Level:

In 2016, the 29$^{\text{th}}$ of February was a Monday. When will be the next leap year when the 29$^{\text{th}}$ of February is a Monday?

This problem is adapted from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.