Secondary Live Problems

Each time you visit the NRICH site there will be some activities which are 'live'. That means we are inviting you to send us your solutions and we will publish a selection of them, along with your name and your school's name. If you'd like to know more about what we're looking for, read this short article.

The last day for sending in solutions to these live problems is Monday 10 July.

Subtraction Surpriselive

Age 7 to 14
Challenge Level

Try out some calculations. Are you surprised by the results?

Non-transitive Dicelive

Age 11 to 14
Challenge Level

Alison and Charlie are playing a game. Charlie wants to go first so Alison lets him. Was that such a good idea?

Pair Productslive

Age 14 to 16
Challenge Level

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

Pick's Theoremlive

Age 14 to 16
Challenge Level

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

Square Remainderslive

Age 16 to 18
Challenge Level

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

Divisible Factorisationslive

Age 16 to 18
Challenge Level

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

Square Differencelive

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?

Proper Factorslive

Age 16 to 18
Challenge Level

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