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 31 January.

Three Neighbourslive

Age 7 to 14Challenge Level

Take three consecutive numbers and add them together. What do you notice?

Age 11 to 16Challenge Level

Is there a quick and easy way to calculate the sum of the first 100 odd numbers?

Where Are the Primes?live

Age 11 to 16Challenge Level

What can we say about all the primes which are greater than 3?

Three Consecutive Odd Numberslive

Age 11 to 16Challenge Level

How many sets of three consecutive odd numbers can you find, in which all three numbers are prime?

What Does it All Add up To?live

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?

Different Productslive

Age 14 to 16Challenge Level

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

Impossible Sumslive

Age 14 to 18Challenge Level

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

Difference of Odd Squareslive

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?

KS5 Proof Shortslive

Age 16 to 18Challenge Level

Here are a few questions taken from the Test of Mathematics for University Admission (or TMUA).

Direct Logiclive

Age 16 to 18Challenge Level

Can you work through these direct proofs, using our interactive proof sorters?

Dodgy Proofslive

Age 16 to 18Challenge Level

These proofs are wrong. Can you see why?

Secondary Toughnutslive

Age 11 to 18Challenge Level

These secondary problems have not yet been solved. Can you be the first?