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Many of the problems in this feature include proof sorting activities which challenge you to rearrange statements in order to recreate clear, rigorous proofs.
The last day for sending in your solutions to the live problems is Monday 31 January.
Plus magazine has a selection of interesting articles about proofs here.
problem
Three neighbours
Age
7 to 14
Challenge level
Take three consecutive numbers and add them together. What do you notice?
problem
Three consecutive odd numbers
Age
11 to 16
Challenge level
How many sets of three consecutive odd numbers can you find, in which all three numbers are prime?
problem
Adding odd numbers
Age
11 to 16
Challenge level
Is there a quick and easy way to calculate the sum of the first 100 odd numbers?
problem
Where are the primes?
Age
11 to 16
Challenge level
What can we say about all the primes which are greater than 3?
problem
What does it all add up to?
Age
11 to 18
Challenge level
If you take four consecutive numbers and add them together, the answer will always be even. What else do you notice?
problem
Different products
Age
14 to 16
Challenge level
Take four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
problem
Impossible sums
Age
14 to 18
Challenge level
Which numbers cannot be written as the sum of two or more consecutive numbers?
problem
Difference of odd squares
Age
14 to 18
Challenge level
$40$ can be written as $7^2 - 3^2.$ Which other numbers can be written as the difference of squares of odd numbers?
We are very grateful to the Heilbronn Institute for Mathematical Research for their generous support for the development of these resources.