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# Post 16 Live Problems and Recent Solutions

### Post 16 Live Problems

### Flipping Twisty MatricesLive

### A Powerful MatrixLive

### Square PairLive

### Two and Four Dimensional NumbersLive

### Fix Me or Crush MeLive

### Matrix MeaningLive

### Transformations for 10Live

### Post 16 Students' Solutions

### Square Remainders

### Divisible Factorisations

### Proper Factors

### Square Difference

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When you visit the NRICH site you may find some activities which are 'live'. This means we are inviting students to send us solutions, and we will publish a selection of them, along with each student's name and their school, a few weeks later. If you'd like to know more about what we're looking for, read this short article.

Age 14 to 18

Challenge Level

Investigate the transformations of the plane given by the 2 by 2 matrices with entries taking all combinations of values 0, -1 and +1.

Age 14 to 18

Challenge Level

What happens when you find the powers of this matrix?

Age 14 to 18

Challenge Level

Explore the shape of a square after it is transformed by the action of a matrix.

Age 16 to 18

Challenge Level

Matrices and Complex Numbers combine to enable us to create four dimensional numbers.

Age 16 to 18

Challenge Level

Can you make matrices which will fix one lucky vector and crush another to zero?

Age 16 to 18

Challenge Level

Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.

Age 16 to 18

Challenge Level

Explore the properties of matrix transformations with these 10 questions.

Take a look at these recently solved problems.

Age 16 to 18

Challenge Level

What is the remainder if you divide a square number by $8$?

Age 16 to 18

Challenge Level

Can you show that $n^5-n^3$ is always divisible by $24$?

Age 16 to 18

Challenge Level

Can you find the smallest integer which has exactly 426 proper factors?

Age 16 to 18

Challenge Level

Which numbers can you write as a difference of two squares? In how many ways can you write $pq$ as a difference of two squares if $p$ and $q$ are prime?