# Reasoning, Justifying, Convincing and Proof - Advanced

### Prime Sequences

##### Age 16 to 18Challenge 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?

### Stats Statements

##### Age 16 to 18Challenge Level

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

### Integration Matcher

##### Age 16 to 18Challenge Level

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

### Impossible Square?

##### Age 16 to 18Challenge Level

Can you make a square from these triangles?

### Dodgy Proofs

##### Age 16 to 18Challenge Level

These proofs are wrong. Can you see why?

### Impossible Triangles?

##### Age 16 to 18Challenge Level

Which of these triangular jigsaws are impossible to finish?

### Polynomial Interpolation

##### Age 16 to 18Challenge Level

Can you fit polynomials through these points?

### What's a Group?

##### Age 16 to 18Challenge 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.

### What Does it All Add up To?

##### Age 11 to 18Challenge Level

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

### Impossible Sums

##### Age 14 to 18Challenge Level

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

### Difference of Odd Squares

##### Age 14 to 18Challenge Level

$40$ can be written as $7^2 - 3^2.$ Which other numbers can be written as the difference of squares of odd numbers?