### 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?

# Algebraic Average

##### Stage: 3 Short Challenge Level:
The sum of the three numbers is 3x, so y + z = 2x. Hence the mean of y and z is x.

Note: If the mean is taken out of a data set, the mean is left unchanged!

This problem is taken from the UKMT Mathematical Challenges.
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