Challenge Level

This group tasks allows you to search for arithmetic progressions in the prime numbers. How many of the challenges will you discover for yourself?

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Are these statistical statements sometimes, always or never true? Or it is impossible to say?

Challenge Level

Can you match the charts of these functions to the charts of their integrals?

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Which of these triangular jigsaws are impossible to finish?

Challenge Level

Explore the properties of some groups such as: The set of all real numbers excluding -1 together with the operation x*y = xy + x + y. Find the identity and the inverse of the element x.

Challenge Level

If you take four consecutive numbers and add them together, the answer will always be even. What else do you notice?

Challenge Level

Which numbers cannot be written as the sum of two or more consecutive numbers?

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?