### Counting Factors

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

### Summing Consecutive Numbers

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

### 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?

# One or Both

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

A maths exam contained only two questions. Problem one was solved by 70% of the pupils. Problem two was solved by 60% of them. Every pupil solved at least one of the problems. Nine pupils solved both problems. How many pupils took the exam?

In the following year the maths exam contained two percentage problems. This time each problem was solved by 72% of the pupils and every pupil got at least one problem right again. What can you say about the number of pupils in the class?

Can you make a problem like this of your own?