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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?
Age 11 to 14
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?
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.