### 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?

### Always the Same

Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?

### Fibs

The well known Fibonacci sequence is 1 ,1, 2, 3, 5, 8, 13, 21.... How many Fibonacci sequences can you find containing the number 196 as one of the terms?

# Even So

##### Stage: 3 Challenge Level:

Find some triples of whole numbers $a$, $b$ and $c$ such that $a^2 + b^2 + c^2$ is a multiple of 4. Is it necessarily the case that $a$, $b$ and $c$ must all be even? If so, can you explain why?