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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?

Top-heavy Pyramids

Age 11 to 14 Challenge Level:

Order the numbers in a variety of ways. Where a number is placed does make a difference.

Look at the first example given. How many times is the 4 used in an addition calculation in the pyramid? What about the 5? And the 7?
Try this with the second example too.
Would it help to make up some larger pyramids and then to repeat this process?
Do you notice a pattern? Could this help?