### Summing Consecutive Numbers

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

### 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?

# The Simple Life

##### Age 11 to 14Challenge Level

For each of the pairs below, there are whole number multiples that combine to give $5x + 8y$:

$$(x + y) \quad (x + 2y)$$$$(x + y) \quad (x + 4y)$$$$(x + 2y) \quad (2x + 3y)$$$$(2x + 3y) \quad (x + y)$$$$(x – 2y) \quad (x + 4y)$$$$(x + y) \quad (x – 2y)$$$$(x + 2y) \quad (x + 4y)$$