### 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?

# Always a Multiple?

##### Age 11 to 14Challenge Level

Watch the video to see Charlie's number trick.

If you can't play the video, you can read a description here.

Try a few examples for yourself. Do you always get a multiple of 11?

Can you explain why?

Alison and Charlie came up with their own explanations:

If you can't play the videos, you can read a description here.

Here are some similar number tricks.
Can you use Charlie's or Alison's representation to explain how they work?

• Take any two-digit number. Reverse the digits, and subtract your answer from your original number. What do you notice?